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
Question ID: 10190010050
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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.
Question ID: 10190010080
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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
Question ID: 10190020020
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c) $27$
a
No
Question ID: 10190020030
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d) $29$
a
Yes
Question ID: 10190020040
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e) $47$
a
Yes
Question ID: 10190020050
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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
Question ID: 10190020080
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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
$2^2\times3$
Question ID: 10190050010
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b) $18$
a
$2\times3^2$
Question ID: 10190050020
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c) $63$
a
$3^2\times7$
Question ID: 10190050030
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d) $50$
a
$2\times5^2$
Question ID: 10190050040
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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
$2^2\times3\times5^2$
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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
$2\times3\times5\times7\times11\times13$
Question ID: 10190090050
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f) $33\,813$
a
$3^2\times13\times17^2$
Question ID: 10190090060
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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
$2^2\times3^2$
Question ID: 10190100040
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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
$1, 2, 3, 4, 6, 12$
Question ID: 10190130020
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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
$3$
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b) $36$
a
$6$
Question ID: 10190140020
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c) $64$
a
$8$
Question ID: 10190140030
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d) $4900$
a
$70$
Question ID: 10190140040
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e) $324$
a
$18$
Question ID: 10190140050
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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
$6$
Question ID: 10190150020
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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
$12$
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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
$5$
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c) $28$
a
$7$
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d) $48$
a
$3$
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e) $60$
a
$15$
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f) $22869$
a
$21$
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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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