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Number - Prime Factorisation

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Question 1


Are the following numbers prime numbers?

a) $4$  a s v d
b) $5$  a s v d
c) $6$  a s v d
d) $7$  a s v d
e) $8$  a s v d
f) $9$  a s v d
g) $10$  a s v d
h) $11$  a s v d


Question 2


Are the following numbers prime numbers?

a) $1$  a s v d
b) $17$  a s v d
c) $27$  a s v d
d) $29$  a s v d
e) $47$  a s v d
f) $51$  a s v d
g) $79$  a s v d
h) $129$  a s v d


Question 3


Express the following as a product of their prime factors

a) $6$  a s v d
b) $10$  a s v d
c) $14$  a s v d
d) $26$  a s v d
e) $33$  a s v d
f) $35$  a s v d


Question 4


Express the following as a product of their prime factors

a) $30$  a s v d
b) $70$  a s v d
c) $105$  a s v d
d) $110$  a s v d
e) $78$  a s v d
f) $231$  a s v d


Question 5


Express the following as a product of their prime factors

a) $12$  a s v d
b) $18$  a s v d
c) $63$  a s v d
d) $50$  a s v d
e) $24$  a s v d
f) $135$  a s v d


Question 6


Express the following as a product of their prime factors

a) $7\times11$  a s v d
b) $2^2\times5$  a s v d
c) $5^2\times11$  a s v d
d) $3\times5\times13$  a s v d
e) $3^2\times13$  a s v d
f) $2\times13\times29$  a s v d


Question 7


Express the following as a product of their prime factors

a) $36$  a s v d
b) $90$  a s v d
c) $100$  a s v d
d) $315$  a s v d
e) $600$  a s v d
f) $2352$  a s v d


Question 8


Which number is represented by the following prime factorisations?

a) $7$  a s v d
b) $23$  a s v d
c) $4$  a s v d
d) $49$  a s v d
e) $101$  a s v d
f) $27$  a s v d


Question 9


Express the following as a product of their prime factors

a) $300$  a s v d
b) $14\,850$  a s v d
c) $14\,300$  a s v d
d) $3267$  a s v d
e) $30\,030$  a s v d
f) $33\,813$  a s v d


Question 10


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

a) $60$  a s v d
b) $84$  a s v d
c) $24$  a s v d
d) $36$  a s v d
e) $6$  a s v d
f) $360$  a s v d


Question 11


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

a) $210$  a s v d
b) $60$  a s v d
c) $150$  a s v d
d) $300$  a s v d
e) $10$  a s v d
f) $900$  a s v d


Question 12


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

a) $720$  a s v d
b) $3600$  a s v d
c) $180$  a s v d
d) $60$  a s v d
e) $30$  a s v d
f) $2160$  a s v d


Question 13


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

a) $30$  a s v d
b) $48$  a s v d
c) $54$  a s v d
d) $90$  a s v d
e) $140$  a s v d
f) $160$  a s v d
g) $312$  a s v d
h) $650$  a s v d


Question 14


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

a) $9$  a s v d
b) $36$  a s v d
c) $64$  a s v d
d) $4900$  a s v d
e) $324$  a s v d
f) $129600$  a s v d


Question 15


By using prime factorisation, find...

a) The cube root of $125$  a s v d

b) The cube root of $216$  a s v d

c) The cube root of $512$  a s v d

d) The fourth root of $1296$  a s v d

e) The fourth root of $160000$  a s v d

f) The fifth root of $248832$  a s v d



Question 16


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

a) $12$  a s v d
b) $20$  a s v d
c) $28$  a s v d
d) $48$  a s v d
e) $60$  a s v d
f) $22869$  a s v d


Question 17


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

a) $108$  a s v d
b) $3$  a s v d
c) $675$  a s v d
d) $3969$  a s v d