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Middle Years

1.07 Prime factorisations

Worksheet
Factor trees
1

Select all the prime numbers from each of these lists:

a

3, 10, 12, 4, 5, 6

b

14, 7, 15, 16, 13, 11

c

21, 19, 27, 17, 22, 1

2

A number has the following factor tree:

What is this number at the top of the tree?

3

A number has the following factor tree:

What is this number at the top of the tree?

4

Construct a factor tree for the following numbers:

a
6
b
12
c
28
d
42
e
81
f
144
g
200
h
360
Prime factorisations
5

Which of the following shows a correct prime factorisation in expanded form?

a

175 = 35 \times 5

b

20 = 2 \times 2 \times 5

c

286 = 2 \times 7 \times 11

d

27 = 3^{3}

6

Which of the following shows a correct prime factorisation in index form?

a

36 = 2 \times 2 \times 2 \times 3

b

770 = 3^{2} \times 55

c

200 = 2^{3} \times 5^{2}

d

21 = 3^{2} \times 7

7

Write the following values as a product of prime factors in expanded form:

a
36
b
42
c
54
d
48
e
72
f
96
g
132
h
148
8

Write the following values as a product of prime factors in index form:

a
90
b
200
c
180
d
225
e
208
f
400
g
560
h
504
9

For the following values:

i

Write as a product of prime factors in expanded form.

ii

Using your answer from part (i), list all the factors.

a

12

b

35

c
20
d
40
e
52
f
54
g
66
h
275
10

List all the factors of 100.

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