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