# Number - Highest Common Factor

**Question 1**

By listing factors for each number, identify the highest common factor for:

a) $4,6$

a
$2$

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Factors of $4$: $1,2,4$

Factors of $6$: $1,2,3,6$

Highest common factor is $2$

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b) $9,12$

a
$3$

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Factors of $9$: $1,3,9$

Factors of $12$: $1,2,3,4,6,12$

Highest common factor is $3$

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c) $10,25$

a
$5$

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Factors of $10$: $1,2,5,10$

Factors of $25$: $1,5,25$

Highest common factor is $5$

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d) $20,28$

a
$4$

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e) $18,42$

a
$6$

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f) $35,63$

a
$7$

Question ID: 10310010060

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g) $10,40$

a
$10$

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h) $33,88$

a
$11$

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**Question 2**

By listing factors for each number, identify the highest common factor for:

a) $6,9,15$

a
$3$

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s
Factors of $6$: $1,2,3,6$

Factors of $9$: $1,3,9$

Factors of $15$: $1,3,5,15$

Highest common factor is $3$

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b) $2,4,8$

a
$2$

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c) $12,24,30$

a
$6$

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d) $32,40,56$

a
$8$

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e) $25,35,65$

a
$5$

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f) $7,28,42$

a
$7$

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g) $48,24,60$

a
$12$

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h) $75,150,45$

a
$15$

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**Question 3**

By finding prime factors, identify the highest common factor for:

a) $12,21$

a
$3$

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Prime factorisation of $12=2^2\times3$

Prime factorisation of $21=3\times7$

Common prime factors are $3$. So the highest common factor is $3$.

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b) $12,18$

a
$6$

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Prime factorisation of $12=2^2\times3$

Prime factorisation of $18=2\times3^2$

Common prime factors are $2\times3$. So the highest common factor is $6$.

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c) $12,38$

a
$4$

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Prime factorisation of $12=2^2\times3$

Prime factorisation of $28=2^2\times7$

Common prime factors are $2^2$. So the highest common factor is $4$.

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d) $15,40$

a
$5$

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e) $30,50$

a
$10$

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f) $16,72$

a
$8$

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g) $49,77$

a
$7$

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h) $12,60$

a
$12$

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i) $36,81$

a
$9$

Question ID: 10310030090

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j) $28,42$

a
$14$

Question ID: 10310030100

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k) $60,135$

a
$15$

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l) $20,180$

a
$20$

Question ID: 10310030120

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m) $39,65$

a
$13$

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n) $60,98$

a
$2$

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o) $36,54$

a
$18$

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p) $66,110$

a
$22$

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**Question 4**

By finding prime factors, identify the highest common factor for:

a) $18,24,30$

a
$6$

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b) $8,20,24$

a
$4$

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c) $18,6,21$

a
$3$

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d) $8,24,16$

a
$8$

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e) $60,20,90$

a
$10$

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f) $15,75,55$

a
$5$

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g) $72,24,108$

a
$12$

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h) $48,80,96$

a
$16$

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**Question 5**

Find the highest common factor for:

a) $75,175$

a
$25$

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b) $63,105$

a
$21$

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c) $48,112$

a
$16$

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d) $46,115,92$

a
$23$

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e) $56,252$

a
$28$

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f) $48,24,132$

a
$12$

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g) $6,78,45$

a
$3$

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h) $266,114$

a
$38$

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**Question 6**

Solve the following problems using your knowledge of Highest Common Factors

a) I have $18$ apples and $24$ oranges. I want to give each friend an indentical basket with apples and oranges in them. What is the greatest number of baskets that I can make and how many of each fruit are in them?

a
I can make $6$ baskets each with $3$ apples and $4$ oranges in.

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b) James is making first aid kits to share with colleagues. He has 20 antiseptic wipes and 12 plasters, which he would like to distribute equally among the kits, with nothing left over. What is the greatest number of kits James can make?

a
James can make $4$ kits with $5$ antiseptic wipes and $3$ plasters in each

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c) There are 60 girls and 36 boys who want to participate in a coding competition. If each team must have the same number of girls and the same number of boys, what is the greatest number of teams that can participate in the competition and how many girls and boys will be on each team?

a
There can be $12$ teams made up of $5$ girls and $3$ boys

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d) Sophie has $70$ pens and $28$ pencil cases. She wants to sell all of the pens and pencil cases in identical packages. What is the greatest number of packages she can make?

a
Sophie can make $14$ packages

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**Question 1**

By listing factors for each number, identify the highest common factor for:

a) $4,6$

b) $9,12$

c) $10,25$

d) $20,28$

e) $18,42$

f) $35,63$

g) $10,40$

h) $33,88$

**Question 2**

By listing factors for each number, identify the highest common factor for:

a) $6,9,15$

b) $2,4,8$

c) $12,24,30$

d) $32,40,56$

e) $25,35,65$

f) $7,28,42$

g) $48,24,60$

h) $75,150,45$

**Question 3**

By finding prime factors, identify the highest common factor for:

a) $12,21$

b) $12,18$

c) $12,38$

d) $15,40$

e) $30,50$

f) $16,72$

g) $49,77$

h) $12,60$

i) $36,81$

j) $28,42$

k) $60,135$

l) $20,180$

m) $39,65$

n) $60,98$

o) $36,54$

p) $66,110$

**Question 4**

By finding prime factors, identify the highest common factor for:

a) $18,24,30$

b) $8,20,24$

c) $18,6,21$

d) $8,24,16$

e) $60,20,90$

f) $15,75,55$

g) $72,24,108$

h) $48,80,96$

**Question 5**

Find the highest common factor for:

a) $75,175$

b) $63,105$

c) $48,112$

d) $46,115,92$

e) $56,252$

f) $48,24,132$

g) $6,78,45$

h) $266,114$

**Question 6**

Solve the following problems using your knowledge of Highest Common Factors

a) I have $18$ apples and $24$ oranges. I want to give each friend an indentical basket with apples and oranges in them. What is the greatest number of baskets that I can make and how many of each fruit are in them?

b) James is making first aid kits to share with colleagues. He has 20 antiseptic wipes and 12 plasters, which he would like to distribute equally among the kits, with nothing left over. What is the greatest number of kits James can make?

c) There are 60 girls and 36 boys who want to participate in a coding competition. If each team must have the same number of girls and the same number of boys, what is the greatest number of teams that can participate in the competition and how many girls and boys will be on each team?

d) Sophie has $70$ pens and $28$ pencil cases. She wants to sell all of the pens and pencil cases in identical packages. What is the greatest number of packages she can make?

__Answers__

**Question 1**

a) $2$

b) $3$

c) $5$

d) $4$

e) $6$

f) $7$

g) $10$

h) $11$

**Question 2**

a) $3$

b) $2$

c) $6$

d) $8$

e) $5$

f) $7$

g) $12$

h) $15$

**Question 3**

a) $3$

b) $6$

c) $4$

d) $5$

e) $10$

f) $8$

g) $7$

h) $12$

i) $9$

j) $14$

k) $15$

l) $20$

m) $13$

n) $2$

o) $18$

p) $22$

**Question 4**

a) $6$

b) $4$

c) $3$

d) $8$

e) $10$

f) $5$

g) $12$

h) $16$

**Question 5**

a) $25$

b) $21$

c) $16$

d) $23$

e) $28$

f) $12$

g) $3$

h) $38$

**Question 6**

a) I can make $6$ baskets each with $3$ apples and $4$ oranges in.

b) James can make $4$ kits with $5$ antiseptic wipes and $3$ plasters in each

c) There can be $12$ teams made up of $5$ girls and $3$ boys

d) Sophie can make $14$ packages

**Question 1**

By listing factors for each number, identify the highest common factor for:

a) $4,6$

b) $9,12$

c) $10,25$

d) $20,28$

e) $18,42$

f) $35,63$

g) $10,40$

h) $33,88$

**Question 2**

By listing factors for each number, identify the highest common factor for:

a) $6,9,15$

b) $2,4,8$

c) $12,24,30$

d) $32,40,56$

e) $25,35,65$

f) $7,28,42$

g) $48,24,60$

h) $75,150,45$

**Question 3**

By finding prime factors, identify the highest common factor for:

a) $12,21$

b) $12,18$

c) $12,38$

d) $15,40$

e) $30,50$

f) $16,72$

g) $49,77$

h) $12,60$

i) $36,81$

j) $28,42$

k) $60,135$

l) $20,180$

m) $39,65$

n) $60,98$

o) $36,54$

p) $66,110$

**Question 4**

By finding prime factors, identify the highest common factor for:

a) $18,24,30$

b) $8,20,24$

c) $18,6,21$

d) $8,24,16$

e) $60,20,90$

f) $15,75,55$

g) $72,24,108$

h) $48,80,96$

**Question 5**

Find the highest common factor for:

a) $75,175$

b) $63,105$

c) $48,112$

d) $46,115,92$

e) $56,252$

f) $48,24,132$

g) $6,78,45$

h) $266,114$

**Question 6**

Solve the following problems using your knowledge of Highest Common Factors

a) I have $18$ apples and $24$ oranges. I want to give each friend an indentical basket with apples and oranges in them. What is the greatest number of baskets that I can make and how many of each fruit are in them?

b) James is making first aid kits to share with colleagues. He has 20 antiseptic wipes and 12 plasters, which he would like to distribute equally among the kits, with nothing left over. What is the greatest number of kits James can make?

c) There are 60 girls and 36 boys who want to participate in a coding competition. If each team must have the same number of girls and the same number of boys, what is the greatest number of teams that can participate in the competition and how many girls and boys will be on each team?

d) Sophie has $70$ pens and $28$ pencil cases. She wants to sell all of the pens and pencil cases in identical packages. What is the greatest number of packages she can make?

__Answers__

**Question 1**

a) $2$

b) $3$

c) $5$

d) $4$

e) $6$

f) $7$

g) $10$

h) $11$

**Question 2**

a) $3$

b) $2$

c) $6$

d) $8$

e) $5$

f) $7$

g) $12$

h) $15$

**Question 3**

a) $3$

b) $6$

c) $4$

d) $5$

e) $10$

f) $8$

g) $7$

h) $12$

i) $9$

j) $14$

k) $15$

l) $20$

m) $13$

n) $2$

o) $18$

p) $22$

**Question 4**

a) $6$

b) $4$

c) $3$

d) $8$

e) $10$

f) $5$

g) $12$

h) $16$

**Question 5**

a) $25$

b) $21$

c) $16$

d) $23$

e) $28$

f) $12$

g) $3$

h) $38$

**Question 6**

a) I can make $6$ baskets each with $3$ apples and $4$ oranges in.

b) James can make $4$ kits with $5$ antiseptic wipes and $3$ plasters in each

c) There can be $12$ teams made up of $5$ girls and $3$ boys

d) Sophie can make $14$ packages

__Solutions__

**Question 1**

a) Factors of $4$: $1,2,4$

Factors of $6$: $1,2,3,6$

Highest common factor is $2$

b) Factors of $9$: $1,3,9$

Factors of $12$: $1,2,3,4,6,12$

Highest common factor is $3$

c) Factors of $10$: $1,2,5,10$

Factors of $25$: $1,5,25$

Highest common factor is $5$

d)

e)

f)

g)

h)

**Question 2**

a) Factors of $6$: $1,2,3,6$

Factors of $9$: $1,3,9$

Factors of $15$: $1,3,5,15$

Highest common factor is $3$

b)

c)

d)

e)

f)

g)

h)

**Question 3**

a) Prime factorisation of $12=2^2\times3$

Prime factorisation of $21=3\times7$

Common prime factors are $3$. So the highest common factor is $3$.

b) Prime factorisation of $12=2^2\times3$

Prime factorisation of $18=2\times3^2$

Common prime factors are $2\times3$. So the highest common factor is $6$.

c) Prime factorisation of $12=2^2\times3$

Prime factorisation of $28=2^2\times7$

Common prime factors are $2^2$. So the highest common factor is $4$.

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

n)

o)

p)

**Question 4**

a)

b)

c)

d)

e)

f)

g)

h)

**Question 5**

a)

b)

c)

d)

e)

f)

g)

h)

**Question 6**

a)

b)

c)

d)