# Prime Factorisations with Indices

In this worksheet, students select the correct prime factorisation for the given numbers.

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Use Concepts and Vocabulary for All Numbers

Difficulty level:

### QUESTION 1 of 10

The list of prime numbers starts as follows:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37........

All other whole numbers are known as composite and can be written as the product of prime factors.

This is known as  prime factorisation

We use indices to tidy up long strings of the same number.

Examples

54 = 2 x 3 x 3 x 3 = 2 x 33

28 = 2 x 2 x 7 = 22 x 7

24 = 2 x 2 x 2 x 3 = 23 x 3

Select the correct prime factorisation for:

20

4 x 5

2 x 2 x 5 x 5

2² x 5

2³ x 5

Select the correct prime factorisation for:

28

3 x 3 x 5

2² x 5

2 x 3²

2² x 7

Select the correct prime factorisation for:

30

2² x 5

2 x 3 x 5

2 x 3² x 5

3 x 10

Select the correct prime factorisation for:

8

2 x 4

2² x 7

Select the correct prime factorisation for:

24

3 x 3 x 5

2³ x 3

2² x 3

2³ x 5

Select the correct prime factorisation for:

40

3² x 5

2² x 5

2 x 2 x 3

2³ x 5

Select the correct prime factorisation for:

44

4 x 11

3² x 2²

2² x 11

2² x 9

Select the correct prime factorisation for:

16

24

28

42

2 x 8

Select the correct prime factorisation for:

56

2³ x 7

2³ x 11

2 x 3 x 7

3³ x 7

Select the correct prime factorisation for:

36

2³ x 3³

2³ x 3

2² x 3²

2² x 9

• Question 1

Select the correct prime factorisation for:

20

CORRECT ANSWER
2² x 5
EDDIE SAYS
Splitting this into prime factors gives 2 x 2 x 5 Next, all you have to do is write your numbers in index form
• Question 2

Select the correct prime factorisation for:

28

CORRECT ANSWER
2² x 7
EDDIE SAYS
Splitting this into prime factors gives 2 x 2 x 7 Next, all you have to do is write your numbers in index form
• Question 3

Select the correct prime factorisation for:

30

CORRECT ANSWER
2 x 3 x 5
EDDIE SAYS
Splitting this into prime factors gives 2 x 3 x 5 You cannot then simplify this using indices as we only have one of each number
• Question 4

Select the correct prime factorisation for:

8

CORRECT ANSWER
EDDIE SAYS
Splitting this into prime factors gives 2 x 2 x 2 Next, all you have to do is write your numbers in index form
• Question 5

Select the correct prime factorisation for:

24

CORRECT ANSWER
2³ x 3
EDDIE SAYS
Splitting this into prime factors gives 2 x 2 x 2 x 3 Next, all you have to do is write your numbers in index form
• Question 6

Select the correct prime factorisation for:

40

CORRECT ANSWER
2³ x 5
EDDIE SAYS
Splitting this into prime factors gives 2 x 2 x 2 x 5 Next, all you have to do is write your numbers in index form
• Question 7

Select the correct prime factorisation for:

44

CORRECT ANSWER
2² x 11
EDDIE SAYS
Splitting this into prime factors gives 2 x 2 x 11 Next, all you have to do is write your numbers in index form
• Question 8

Select the correct prime factorisation for:

16

CORRECT ANSWER
24
EDDIE SAYS
Splitting this into prime factors gives 2 x 2 x 2 x 2 Next, all you have to do is write your numbers in index form
• Question 9

Select the correct prime factorisation for:

56

CORRECT ANSWER
2³ x 7
EDDIE SAYS
Splitting this into prime factors gives 2 x 2 x 2 x 7 Next, all you have to do is write your numbers in index form
• Question 10

Select the correct prime factorisation for:

36

CORRECT ANSWER
2² x 3²
EDDIE SAYS
Splitting this into prime factors gives 2 x 2 x 3 x 3 Next, all you have to do is write your numbers in index form
---- OR ----

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