__Answers__

**Question 1**

a) $1,2,3,6$

b) $1,2,4,8$

c) $1,2,5,10$

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

e) $1,2,4,5,10,20$

f) $1,5,25$

g) $1,3,5,9,15,45$

h) $1,2,3,4,6,8,9,12,18,24,36,72$

**Question 2**

a) $1,2$

b) $1,5$

c) $1,11$

d) $1,17$

e) $1,29$

f) They are all prime numbers. The definition of a prime number is that it has two factors ($1$ and itself). Therefore they will always produce $2$ factors.

**Question 3**

a) $1,3,9$

b) $1,2,3,4,6,9,12,18,36$

c) $1,7,49$

d) $1,3,9,27,81$

e) $1,2,4,5,10,20,25,50,100$

f) They are all square numbers. They will produce an odd number of factors as one of their factors when squared gives the number.

**Question 4**

a) $1,2,5,10,25,50$

b) $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

c) $1, 2, 4, 8, 11, 22, 44, 88$

d) $1, 5, 19, 95$

e) $1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$

f) $1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180$

**Question 5**

a) $0,3,6,9,12$

b) $0,5,10,15,20$

c) $0,10,20,30,40$

d) $0,9,18,27,36$

e) $0,7,14,21,28$

f) $0,12,24,26,48$

**Question 6**

a) $0,6,12,18,24,30,36,42,48,54$

b) $0,11,22,33,44,55,66,77,88,99$

c) $0,20,40,60,80,100,120,140,160,180$

d) $0,25,50,75,100,125,150,175,200,225$

e) $0,1000,2000,3000,4000,5000,6000,7000,8000,9000$

f) $0,17,34,51,68,85,102,119,136,153$

**Question 7**

a) True

b) False

c) True

d) True

e) False

f) True

**Question 8**

a) True

b) False

c) True

d) True

e) True

f) False

**Question 9**

a) Prime

b) Composite

c) Prime

d) Prime

e) Prime

f) Composite

**Question 10**

a) $-15,-5,-3,-1,1,3,5,15$

b) $-24,-12,-8,-6,-4,-3,-2,-1,1,2,3,4,6,8,12,24$

c) $-28,-14,-7,-4,-2,-1,1,2,4,7,14,28$

d) $-30,-15,-10,-6,-5,-3,-2,-1,1,2,3,5,6,10,15,30$

e) $-55,-11,-5,-1,1,5,11,55$

f) $-1, -2, -3, -6, -13, -26, -39, -78,1, 2, 3, 6, 13, 26, 39, 78$

**Question 11**

a) $-10,-8,-6,-4,-2,0,2,4,6,8,10$

b) $-25,-20,-15,-10,-5,0,5,10,15,20,25$

c) $-50,-40,-30,-20,-10,0,10,20,30,40,50$

d) $-55,-44,-33,-22,-11,0,11,22,33,44,55$

e) $-45,-36,-27,-18,-9,0,9,18,27,36,45$

f) $-95,-76,-57,-38,-19,0,19,38,57,76,95$

**Question 1**

List all factors for the following numbers:

a) $6$

b) $8$

c) $10$

d) $12$

e) $20$

f) $25$

g) $45$

h) $72$

**Question 2**

List all factors for the following numbers:

a) $2$

b) $5$

c) $11$

d) $17$

e) $29$

f) What is special about these numbers? How many factors do they produce?

**Question 3**

List all factors for the following numbers:

a) $9$

b) $36$

c) $49$

d) $81$

e) $100$

f) What is special about these numbers? How many factors do they produce?

**Question 4**

List all factors for the following numbers:

a) $50$

b) $60$

c) $88$

d) $95$

e) $120$

f) $180$

**Question 5**

List the first $5$ multiples for the following numbers (

**remember $0$!**):

a) $3$

b) $5$

c) $10$

d) $9$

e) $7$

f) $12$

**Question 6**

List the first $10$ multiples for the following numbers:

a) $6$

b) $11$

c) $20$

d) $25$

e) $1000$

f) $17$

**Question 7**

Are the following statements true or false?

a) $2$ is a factor of $18$

b) $3$ is a factor of $19$

c) $5$ is a factor of $75$

d) $14$ is a factor of $140$

e) $4$ is a factor of $86$

f) $11$ is a factor of $143$

**Question 8**

Are the following statements true or false?

a) $12$ is a multiple of $4$

b) $29$ is a multiple of $3$

c) $0$ is a multiple of $104$

d) $36$ is a multiple of $9$

e) $45$ is a multiple of $15$

f) $48$ is a multiple of $13$

**Question 9**

Classify the following numbers as prime or composite:

a) $5$

b) $6$

c) $11$

d) $29$

e) $37$

f) $87$

**Question 10**

Negative numbers can also be factors! Using this information find the factors for:

a) $15$

b) $24$

c) $28$

d) $30$

e) $55$

f) $78$

**Question 11**

Negative numbers can also be multiples! Using this information find the $11$ multiples of the following numbers nearest $0$ ($5$ multiples above and below $0$):

a) $2$

b) $5$

c) $10$

d) $11$

e) $9$

f) $19$

__Answers__

**Question 1**

a) $1,2,3,6$

b) $1,2,4,8$

c) $1,2,5,10$

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

e) $1,2,4,5,10,20$

f) $1,5,25$

g) $1,3,5,9,15,45$

h) $1,2,3,4,6,8,9,12,18,24,36,72$

**Question 2**

a) $1,2$

b) $1,5$

c) $1,11$

d) $1,17$

e) $1,29$

f) They are all prime numbers. The definition of a prime number is that it has two factors ($1$ and itself). Therefore they will always produce $2$ factors.

**Question 3**

a) $1,3,9$

b) $1,2,3,4,6,9,12,18,36$

c) $1,7,49$

d) $1,3,9,27,81$

e) $1,2,4,5,10,20,25,50,100$

f) They are all square numbers. They will produce an odd number of factors as one of their factors when squared gives the number.

**Question 4**

a) $1,2,5,10,25,50$

b) $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

c) $1, 2, 4, 8, 11, 22, 44, 88$

d) $1, 5, 19, 95$

e) $1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$

f) $1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180$

**Question 5**

a) $0,3,6,9,12$

b) $0,5,10,15,20$

c) $0,10,20,30,40$

d) $0,9,18,27,36$

e) $0,7,14,21,28$

f) $0,12,24,26,48$

**Question 6**

a) $0,6,12,18,24,30,36,42,48,54$

b) $0,11,22,33,44,55,66,77,88,99$

c) $0,20,40,60,80,100,120,140,160,180$

d) $0,25,50,75,100,125,150,175,200,225$

e) $0,1000,2000,3000,4000,5000,6000,7000,8000,9000$

f) $0,17,34,51,68,85,102,119,136,153$

**Question 7**

a) True

b) False

c) True

d) True

e) False

f) True

**Question 8**

a) True

b) False

c) True

d) True

e) True

f) False

**Question 9**

a) Prime

b) Composite

c) Prime

d) Prime

e) Prime

f) Composite

**Question 10**

a) $-15,-5,-3,-1,1,3,5,15$

b) $-24,-12,-8,-6,-4,-3,-2,-1,1,2,3,4,6,8,12,24$

c) $-28,-14,-7,-4,-2,-1,1,2,4,7,14,28$

d) $-30,-15,-10,-6,-5,-3,-2,-1,1,2,3,5,6,10,15,30$

e) $-55,-11,-5,-1,1,5,11,55$

f) $-1, -2, -3, -6, -13, -26, -39, -78,1, 2, 3, 6, 13, 26, 39, 78$

**Question 11**

a) $-10,-8,-6,-4,-2,0,2,4,6,8,10$

b) $-25,-20,-15,-10,-5,0,5,10,15,20,25$

c) $-50,-40,-30,-20,-10,0,10,20,30,40,50$

d) $-55,-44,-33,-22,-11,0,11,22,33,44,55$

e) $-45,-36,-27,-18,-9,0,9,18,27,36,45$

f) $-95,-76,-57,-38,-19,0,19,38,57,76,95$