# Number - Prime Factorisation

**Question 1**

Are the following numbers prime numbers?

a) $4$

a
No

Question ID: 10190010010

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Prime numbers can only be divided by $1$ and itself. $4$ can be divided by $1$, $2$ and $4$ so is not a prime number.

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b) $5$

a
Yes

Question ID: 10190010020

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Prime numbers can only be divided by $1$ and itself. $5$ can be divided by $1$ and $5$ only so is a prime number.

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c) $6$

a
No

Question ID: 10190010030

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Prime numbers can only be divided by $1$ and itself. $6$ can be divided by $1$, $2$, $3$ and $6$ so is not a prime number.

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d) $7$

a
Yes

Question ID: 10190010040

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Prime numbers can only be divided by $1$ and itself. $7$ can be divided by $1$ and $7$ only so is a prime number.

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e) $8$

a
No

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Prime numbers can only be divided by $1$ and itself. $8$ can be divided by $1$, $2$ and $4$ and $8$ so is not a prime number.

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f) $9$

a
No

Question ID: 10190010060

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Prime numbers can only be divided by $1$ and itself. $9$ can be divided by $1$, $3$ and $9$ so is not a prime number.

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g) $10$

a
No

Question ID: 10190010070

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Prime numbers can only be divided by $1$ and itself. $10$ can be divided by $1$, $2$, $5$ and $10$ so is not a prime number.

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h) $11$

a
Yes

Question ID: 10190010080

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Prime numbers can only be divided by $1$ and itself. $11$ can be divided by $1$ and $11$ only so is a prime number.

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**Question 2**

Are the following numbers prime numbers?

a) $1$

a
No

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It is tricky to explain why $1$ is not a prime number. Prime numbers can only be divided by $1$ and itself. $1$ is divisible by $1$ only which is itself. Therefore it is not prime.

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b) $17$

a
Yes

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c) $27$

a
No

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d) $29$

a
Yes

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e) $47$

a
Yes

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f) $51$

a
No

Question ID: 10190020060

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g) $79$

a
Yes

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h) $129$

a
No

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**Question 3**

Express the following as a product of their prime factors

a) $6$

a
$2\times3$

Question ID: 10190030010

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b) $10$

a
$2\times5$

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c) $14$

a
$2\times7$

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d) $26$

a
$2\times13$

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e) $33$

a
$3\times11$

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f) $35$

a
$5\times7$

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**Question 4**

Express the following as a product of their prime factors

a) $30$

a
$2\times3\times5$

Question ID: 10190040010

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b) $70$

a
$2\times5\times7$

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c) $105$

a
$3\times5\times7$

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d) $110$

a
$2\times5\times11$

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e) $78$

a
$2\times3\times13$

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f) $231$

a
$3\times7\times11$

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**Question 5**

Express the following as a product of their prime factors

a) $12$

a
$2^2\times3$

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b) $18$

a
$2\times3^2$

Question ID: 10190050020

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c) $63$

a
$3^2\times7$

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d) $50$

a
$2\times5^2$

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e) $24$

a
$2^3\times3$

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f) $135$

a
$3^3\times5$

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**Question 6**

Express the following as a product of their prime factors

a) $7\times11$

a
$77$

Question ID: 10190060010

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b) $2^2\times5$

a
$20$

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c) $5^2\times11$

a
$275$

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d) $3\times5\times13$

a
$195$

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e) $3^2\times13$

a
$117$

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f) $2\times13\times29$

a
$754$

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**Question 7**

Express the following as a product of their prime factors

a) $36$

a
$2^2\times3^2$

Question ID: 10190070010

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b) $90$

a
$2\times3^2\times5$

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c) $100$

a
$2^2\times5^2$

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d) $315$

a
$3^2\times5\times7$

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e) $600$

a
$2^3\times3\times5^2$

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f) $2352$

a
$2^4\times3\times7^2$

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**Question 8**

Which number is represented by the following prime factorisations?

a) $7$

a
$7$

Question ID: 10190080010

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b) $23$

a
$23$

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c) $4$

a
$2^2$

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d) $49$

a
$7^2$

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e) $101$

a
$101$

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f) $27$

a
$3^3$

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**Question 9**

Express the following as a product of their prime factors

a) $300$

a
$2^2\times3\times5^2$

Question ID: 10190090010

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b) $14\,850$

a
$2\times3^3\times5^2\times11$

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c) $14\,300$

a
$2^2\times5^2\times11\times13$

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d) $3267$

a
$3^3\times11^2$

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e) $30\,030$

a
$2\times3\times5\times7\times11\times13$

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f) $33\,813$

a
$3^2\times13\times17^2$

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**Question 10**

It is known that $12=2^2\times3$. Use this to find the prime factorisation of:

a) $60$

a
$2^2\times3\times5$

Question ID: 10190100010

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b) $84$

a
$2^2\times3\times7$

Question ID: 10190100020

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c) $24$

a
$2^3\times3$

Question ID: 10190100030

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d) $36$

a
$2^2\times3^2$

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e) $6$

a
$2\times3$

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f) $360$

a
$2^3\times3^2\times5$

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**Question 11**

It is known that $30=2\times3\times5$. Use this to find the prime factorisation of:

a) $210$

a
$2\times3\times5\times7$

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b) $60$

a
$2^2\times3\times5$

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c) $150$

a
$2\times3\times5^2$

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d) $300$

a
$2^2\times3\times5^2$

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e) $10$

a
$2\times5$

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f) $900$

a
$2^2\times3^2\times5^2$

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**Question 12**

It is known that $360=2^3\times3^2\times5$. Use this to find the prime factorisation of:

a) $720$

a
$2^4\times3^2\times5$

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b) $3600$

a
$2^4\times3^2\times5^2$

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c) $180$

a
$2^2\times3^2\times5$

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d) $60$

a
$2\times3\times5$

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e) $30$

a
$2\times3\times5$

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f) $2160$

a
$2^4\times3^3\times5$

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**Question 13**

By using prime factorisation, list all the positive factors for:

a) $30$

a
$1,2,3,5,6,10,15,30$

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b) $48$

a
$1, 2, 3, 4, 6, 12$

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c) $54$

a
$1, 2, 3, 6, 9, 18, 27, 54$

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d) $90$

a
$1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

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e) $140$

a
$1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140$

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f) $160$

a
$1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160$

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g) $312$

a
$1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312$

Question ID: 10190130070

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h) $650$

a
$1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650$

Question ID: 10190130080

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**Question 14**

By using prime factorisation, find the square root of the following:

a) $9$

a
$3$

Question ID: 10190140010

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b) $36$

a
$6$

Question ID: 10190140020

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c) $64$

a
$8$

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d) $4900$

a
$70$

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e) $324$

a
$18$

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f) $129600$

a
$360$

Question ID: 10190140060

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**Question 15**

By using prime factorisation, find...

a) The cube root of $125$

a
$5$

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b) The cube root of $216$

a
$6$

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c) The cube root of $512$

a
$8$

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d) The fourth root of $1296$

a
$6$

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e) The fourth root of $160000$

a
$20$

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f) The fifth root of $248832$

a
$12$

Question ID: 10190150060

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**Question 16**

What is the lowest multiplier needed in order to make the following square numbers:

a) $12$

a
$3$

Question ID: 10190160010

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b) $20$

a
$5$

Question ID: 10190160020

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c) $28$

a
$7$

Question ID: 10190160030

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d) $48$

a
$3$

Question ID: 10190160040

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e) $60$

a
$15$

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f) $22869$

a
$21$

Question ID: 10190160060

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**Question 17**

What is the lowest multiplier needed in order to make the following cube numbers:

a) $108$

a
$2$

Question ID: 10190170010

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b) $3$

a
$9$

Question ID: 10190170020

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c) $675$

a
$5$

Question ID: 10190170030

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d) $3969$

a
$63$

Question ID: 10190170040

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**Question 1**

Are the following numbers prime numbers?

a) $4$

b) $5$

c) $6$

d) $7$

e) $8$

f) $9$

g) $10$

h) $11$

**Question 2**

Are the following numbers prime numbers?

a) $1$

b) $17$

c) $27$

d) $29$

e) $47$

f) $51$

g) $79$

h) $129$

**Question 3**

Express the following as a product of their prime factors

a) $6$

b) $10$

c) $14$

d) $26$

e) $33$

f) $35$

**Question 4**

Express the following as a product of their prime factors

a) $30$

b) $70$

c) $105$

d) $110$

e) $78$

f) $231$

**Question 5**

Express the following as a product of their prime factors

a) $12$

b) $18$

c) $63$

d) $50$

e) $24$

f) $135$

**Question 6**

Express the following as a product of their prime factors

a) $7\times11$

b) $2^2\times5$

c) $5^2\times11$

d) $3\times5\times13$

e) $3^2\times13$

f) $2\times13\times29$

**Question 7**

Express the following as a product of their prime factors

a) $36$

b) $90$

c) $100$

d) $315$

e) $600$

f) $2352$

**Question 8**

Which number is represented by the following prime factorisations?

a) $7$

b) $23$

c) $4$

d) $49$

e) $101$

f) $27$

**Question 9**

Express the following as a product of their prime factors

a) $300$

b) $14\,850$

c) $14\,300$

d) $3267$

e) $30\,030$

f) $33\,813$

**Question 10**

It is known that $12=2^2\times3$. Use this to find the prime factorisation of:

a) $60$

b) $84$

c) $24$

d) $36$

e) $6$

f) $360$

**Question 11**

It is known that $30=2\times3\times5$. Use this to find the prime factorisation of:

a) $210$

b) $60$

c) $150$

d) $300$

e) $10$

f) $900$

**Question 12**

It is known that $360=2^3\times3^2\times5$. Use this to find the prime factorisation of:

a) $720$

b) $3600$

c) $180$

d) $60$

e) $30$

f) $2160$

**Question 13**

By using prime factorisation, list all the positive factors for:

a) $30$

b) $48$

c) $54$

d) $90$

e) $140$

f) $160$

g) $312$

h) $650$

**Question 14**

By using prime factorisation, find the square root of the following:

a) $9$

b) $36$

c) $64$

d) $4900$

e) $324$

f) $129600$

**Question 15**

By using prime factorisation, find...

a) The cube root of $125$

b) The cube root of $216$

c) The cube root of $512$

d) The fourth root of $1296$

e) The fourth root of $160000$

f) The fifth root of $248832$

**Question 16**

What is the lowest multiplier needed in order to make the following square numbers:

a) $12$

b) $20$

c) $28$

d) $48$

e) $60$

f) $22869$

**Question 17**

What is the lowest multiplier needed in order to make the following cube numbers:

a) $108$

b) $3$

c) $675$

d) $3969$

__Answers__

**Question 1**

a) No

b) Yes

c) No

d) Yes

e) No

f) No

g) No

h) Yes

**Question 2**

a) No

b) Yes

c) No

d) Yes

e) Yes

f) No

g) Yes

h) No

**Question 3**

a) $2\times3$

b) $2\times5$

c) $2\times7$

d) $2\times13$

e) $3\times11$

f) $5\times7$

**Question 4**

a) $2\times3\times5$

b) $2\times5\times7$

c) $3\times5\times7$

d) $2\times5\times11$

e) $2\times3\times13$

f) $3\times7\times11$

**Question 5**

a) $2^2\times3$

b) $2\times3^2$

c) $3^2\times7$

d) $2\times5^2$

e) $2^3\times3$

f) $3^3\times5$

**Question 6**

a) $77$

b) $20$

c) $275$

d) $195$

e) $117$

f) $754$

**Question 7**

a) $2^2\times3^2$

b) $2\times3^2\times5$

c) $2^2\times5^2$

d) $3^2\times5\times7$

e) $2^3\times3\times5^2$

f) $2^4\times3\times7^2$

**Question 8**

a) $7$

b) $23$

c) $2^2$

d) $7^2$

e) $101$

f) $3^3$

**Question 9**

a) $2^2\times3\times5^2$

b) $2\times3^3\times5^2\times11$

c) $2^2\times5^2\times11\times13$

d) $3^3\times11^2$

e) $2\times3\times5\times7\times11\times13$

f) $3^2\times13\times17^2$

**Question 10**

a) $2^2\times3\times5$

b) $2^2\times3\times7$

c) $2^3\times3$

d) $2^2\times3^2$

e) $2\times3$

f) $2^3\times3^2\times5$

**Question 11**

a) $2\times3\times5\times7$

b) $2^2\times3\times5$

c) $2\times3\times5^2$

d) $2^2\times3\times5^2$

e) $2\times5$

f) $2^2\times3^2\times5^2$

**Question 12**

a) $2^4\times3^2\times5$

b) $2^4\times3^2\times5^2$

c) $2^2\times3^2\times5$

d) $2\times3\times5$

e) $2\times3\times5$

f) $2^4\times3^3\times5$

**Question 13**

a) $1,2,3,5,6,10,15,30$

b) $1, 2, 3, 4, 6, 12$

c) $1, 2, 3, 6, 9, 18, 27, 54$

d) $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

e) $1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140$

f) $1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160$

g) $1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312$

h) $1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650$

**Question 14**

a) $3$

b) $6$

c) $8$

d) $70$

e) $18$

f) $360$

**Question 15**

a) $5$

b) $6$

c) $8$

d) $6$

e) $20$

f) $12$

**Question 16**

a) $3$

b) $5$

c) $7$

d) $3$

e) $15$

f) $21$

**Question 17**

a) $2$

b) $9$

c) $5$

d) $63$

**Question 1**

Are the following numbers prime numbers?

a) $4$

b) $5$

c) $6$

d) $7$

e) $8$

f) $9$

g) $10$

h) $11$

**Question 2**

Are the following numbers prime numbers?

a) $1$

b) $17$

c) $27$

d) $29$

e) $47$

f) $51$

g) $79$

h) $129$

**Question 3**

Express the following as a product of their prime factors

a) $6$

b) $10$

c) $14$

d) $26$

e) $33$

f) $35$

**Question 4**

Express the following as a product of their prime factors

a) $30$

b) $70$

c) $105$

d) $110$

e) $78$

f) $231$

**Question 5**

Express the following as a product of their prime factors

a) $12$

b) $18$

c) $63$

d) $50$

e) $24$

f) $135$

**Question 6**

Express the following as a product of their prime factors

a) $7\times11$

b) $2^2\times5$

c) $5^2\times11$

d) $3\times5\times13$

e) $3^2\times13$

f) $2\times13\times29$

**Question 7**

Express the following as a product of their prime factors

a) $36$

b) $90$

c) $100$

d) $315$

e) $600$

f) $2352$

**Question 8**

Which number is represented by the following prime factorisations?

a) $7$

b) $23$

c) $4$

d) $49$

e) $101$

f) $27$

**Question 9**

Express the following as a product of their prime factors

a) $300$

b) $14\,850$

c) $14\,300$

d) $3267$

e) $30\,030$

f) $33\,813$

**Question 10**

It is known that $12=2^2\times3$. Use this to find the prime factorisation of:

a) $60$

b) $84$

c) $24$

d) $36$

e) $6$

f) $360$

**Question 11**

It is known that $30=2\times3\times5$. Use this to find the prime factorisation of:

a) $210$

b) $60$

c) $150$

d) $300$

e) $10$

f) $900$

**Question 12**

It is known that $360=2^3\times3^2\times5$. Use this to find the prime factorisation of:

a) $720$

b) $3600$

c) $180$

d) $60$

e) $30$

f) $2160$

**Question 13**

By using prime factorisation, list all the positive factors for:

a) $30$

b) $48$

c) $54$

d) $90$

e) $140$

f) $160$

g) $312$

h) $650$

**Question 14**

By using prime factorisation, find the square root of the following:

a) $9$

b) $36$

c) $64$

d) $4900$

e) $324$

f) $129600$

**Question 15**

By using prime factorisation, find...

a) The cube root of $125$

b) The cube root of $216$

c) The cube root of $512$

d) The fourth root of $1296$

e) The fourth root of $160000$

f) The fifth root of $248832$

**Question 16**

What is the lowest multiplier needed in order to make the following square numbers:

a) $12$

b) $20$

c) $28$

d) $48$

e) $60$

f) $22869$

**Question 17**

What is the lowest multiplier needed in order to make the following cube numbers:

a) $108$

b) $3$

c) $675$

d) $3969$

__Answers__

**Question 1**

a) No

b) Yes

c) No

d) Yes

e) No

f) No

g) No

h) Yes

**Question 2**

a) No

b) Yes

c) No

d) Yes

e) Yes

f) No

g) Yes

h) No

**Question 3**

a) $2\times3$

b) $2\times5$

c) $2\times7$

d) $2\times13$

e) $3\times11$

f) $5\times7$

**Question 4**

a) $2\times3\times5$

b) $2\times5\times7$

c) $3\times5\times7$

d) $2\times5\times11$

e) $2\times3\times13$

f) $3\times7\times11$

**Question 5**

a) $2^2\times3$

b) $2\times3^2$

c) $3^2\times7$

d) $2\times5^2$

e) $2^3\times3$

f) $3^3\times5$

**Question 6**

a) $77$

b) $20$

c) $275$

d) $195$

e) $117$

f) $754$

**Question 7**

a) $2^2\times3^2$

b) $2\times3^2\times5$

c) $2^2\times5^2$

d) $3^2\times5\times7$

e) $2^3\times3\times5^2$

f) $2^4\times3\times7^2$

**Question 8**

a) $7$

b) $23$

c) $2^2$

d) $7^2$

e) $101$

f) $3^3$

**Question 9**

a) $2^2\times3\times5^2$

b) $2\times3^3\times5^2\times11$

c) $2^2\times5^2\times11\times13$

d) $3^3\times11^2$

e) $2\times3\times5\times7\times11\times13$

f) $3^2\times13\times17^2$

**Question 10**

a) $2^2\times3\times5$

b) $2^2\times3\times7$

c) $2^3\times3$

d) $2^2\times3^2$

e) $2\times3$

f) $2^3\times3^2\times5$

**Question 11**

a) $2\times3\times5\times7$

b) $2^2\times3\times5$

c) $2\times3\times5^2$

d) $2^2\times3\times5^2$

e) $2\times5$

f) $2^2\times3^2\times5^2$

**Question 12**

a) $2^4\times3^2\times5$

b) $2^4\times3^2\times5^2$

c) $2^2\times3^2\times5$

d) $2\times3\times5$

e) $2\times3\times5$

f) $2^4\times3^3\times5$

**Question 13**

a) $1,2,3,5,6,10,15,30$

b) $1, 2, 3, 4, 6, 12$

c) $1, 2, 3, 6, 9, 18, 27, 54$

d) $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

e) $1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140$

f) $1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160$

g) $1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312$

h) $1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650$

**Question 14**

a) $3$

b) $6$

c) $8$

d) $70$

e) $18$

f) $360$

**Question 15**

a) $5$

b) $6$

c) $8$

d) $6$

e) $20$

f) $12$

**Question 16**

a) $3$

b) $5$

c) $7$

d) $3$

e) $15$

f) $21$

**Question 17**

a) $2$

b) $9$

c) $5$

d) $63$

__Solutions__

**Question 1**

a) Prime numbers can only be divided by $1$ and itself. $4$ can be divided by $1$, $2$ and $4$ so is not a prime number.

b) Prime numbers can only be divided by $1$ and itself. $5$ can be divided by $1$ and $5$ only so is a prime number.

c) Prime numbers can only be divided by $1$ and itself. $6$ can be divided by $1$, $2$, $3$ and $6$ so is not a prime number.

d) Prime numbers can only be divided by $1$ and itself. $7$ can be divided by $1$ and $7$ only so is a prime number.

e) Prime numbers can only be divided by $1$ and itself. $8$ can be divided by $1$, $2$ and $4$ and $8$ so is not a prime number.

f) Prime numbers can only be divided by $1$ and itself. $9$ can be divided by $1$, $3$ and $9$ so is not a prime number.

g) Prime numbers can only be divided by $1$ and itself. $10$ can be divided by $1$, $2$, $5$ and $10$ so is not a prime number.

h) Prime numbers can only be divided by $1$ and itself. $11$ can be divided by $1$ and $11$ only so is a prime number.

**Question 2**

a) It is tricky to explain why $1$ is not a prime number. Prime numbers can only be divided by $1$ and itself. $1$ is divisible by $1$ only which is itself. Therefore it is not prime.

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