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Number

Factors and Multiples

1

Match Factor Pairs (A)

Draw a line to match each number to its factor pair.

12
18
24
30
6 × 5
3 × 4
2 × 9
4 × 6
2

Match Factor Pairs (B)

Draw a line to match each number to its factor pair.

15
20
28
36
4 × 5
4 × 7
3 × 5
6 × 6
3

Is It a Factor? (A)

Circle the number that IS a factor of the given number.

Which is a factor of 20?

3
4
6

Which is a factor of 15?

2
4
5

Which is a factor of 36?

5
7
9

Which is a factor of 28?

3
7
9
4

Is It a Factor? (B)

Circle the number that IS a factor of the given number.

Which is a factor of 42?

4
5
7

Which is a factor of 56?

3
8
9

Which is a factor of 45?

4
6
9

Which is a factor of 32?

3
5
8
5

Factor Pairs of 24

24 can be split into two factors. Find the missing factor.

24
1
?
24
2
?
24
3
?
24
4
?
24
6
?
24
8
?
6

Factor Pairs of 36

36 can be split into two factors. Find the missing factor.

36
1
?
36
2
?
36
3
?
36
4
?
36
6
?
36
9
?
7

Multiples of 3

Fill in the missing multiples of 3.

3
6
12
15
?
18
24
27
?
?
8

Multiples of 4

Fill in the missing multiples of 4.

4
8
16
20
?
24
32
36
?
?
9

Is It a Multiple? (A)

Circle YES if the number is a multiple, or NO if it is not.

Is 18 a multiple of 3?

YES
NO

Is 25 a multiple of 4?

YES
NO

Is 35 a multiple of 7?

YES
NO

Is 22 a multiple of 6?

YES
NO
10

Sort: Factors of 12

Sort each number: is it a factor of 12 or not?

1
2
3
4
5
6
7
8
Factor of 12
NOT a factor of 12
11

Arrays Show Factors

Each array shows a factor pair. Count the rows and columns.

?
?
?
?
12

Match Numbers to Their Factors

Draw a line from each number to ALL its factors listed.

10
16
21
25
1, 3, 7, 21
1, 2, 5, 10
1, 5, 25
1, 2, 4, 8, 16
13

Multiples of 6

Fill in the missing multiples of 6.

6
12
24
30
?
36
48
54
?
?
14

Multiples of 7

Fill in the missing multiples of 7.

7
14
28
35
?
42
56
63
?
?
15

Multiples of 8

Fill in the missing multiples of 8.

8
16
32
40
?
48
64
72
?
?
16

Multiples of 9

Fill in the missing multiples of 9.

9
18
36
45
?
54
72
81
?
?
17

Sort: Multiples of 4 or Multiples of 5?

Write each number in the correct column.

20
16
25
32
35
40
Multiples of 4
Multiples of 5
18

Sort: Multiples of 3 or Multiples of 7?

Write each number in the correct column. Some may belong to both!

21
18
14
42
27
49
Multiples of 3 only
Multiples of 7 only
Both
19

Is It a Multiple? (B)

Circle YES or NO.

Is 54 a multiple of 6?

YES
NO

Is 63 a multiple of 8?

YES
NO

Is 48 a multiple of 6?

YES
NO

Is 55 a multiple of 9?

YES
NO
20

Factor Pairs of 48

Find the missing factor for 48.

48
1
?
48
2
?
48
3
?
48
4
?
48
6
?
48
8
?
21

Factor Pairs of 60

Find the missing factor for 60.

60
1
?
60
2
?
60
3
?
60
4
?
60
5
?
60
6
?
22

List the First 5 Multiples

Write the first 5 multiples of each number.

Multiples of 6: ___, ___, ___, ___, ___

Multiples of 8: ___, ___, ___, ___, ___

Multiples of 9: ___, ___, ___, ___, ___

Multiples of 12: ___, ___, ___, ___, ___

23

Common Multiples

Circle the number that is a common multiple of BOTH numbers.

Common multiple of 3 and 4?

8
12
9

Common multiple of 2 and 5?

15
8
10

Common multiple of 4 and 6?

12
8
18

Common multiple of 3 and 5?

10
15
12
24

Factors and Multiples Vocabulary

Use the words 'factor' and 'multiple' to complete each sentence.

3 is a ___ of 12 because 3 × 4 = 12.

20 is a ___ of 5 because 5 × 4 = 20.

7 is a ___ of 49 because 7 × 7 = 49.

72 is a ___ of 8 because 8 × 9 = 72.

25

List All Factor Pairs (A)

Write all factor pairs for each number. Example: 12 → 1×12, 2×6, 3×4.

Factor pairs of 24: ___

Factor pairs of 36: ___

Factor pairs of 48: ___

26

List All Factor Pairs (B)

Write all factor pairs for each number.

Factor pairs of 30: ___

Factor pairs of 42: ___

Factor pairs of 56: ___

27

List All Factors

List ALL factors of each number (not pairs, just the individual factors).

Factors of 40: ___

Factors of 50: ___

Factors of 72: ___

Factors of 100: ___

28

True or False? Factors and Multiples (A)

Circle TRUE or FALSE.

7 is a factor of 42

TRUE
FALSE

50 is a multiple of 8

TRUE
FALSE

Every number is a factor of itself

TRUE
FALSE

1 is a factor of every number

TRUE
FALSE
29

True or False? Factors and Multiples (B)

Circle TRUE or FALSE.

0 is a multiple of every number

TRUE
FALSE

A number can be both a factor and a multiple of itself

TRUE
FALSE

Every even number is a multiple of 2

TRUE
FALSE

13 has exactly two factors

TRUE
FALSE
30

Sort: Prime or Composite?

A prime number has exactly 2 factors (1 and itself). Sort these numbers.

7
12
11
15
23
25
2
9
Prime
Composite
31

Common Factors

List all common factors of each pair of numbers.

Factors of 12: ___ Factors of 18: ___ Common factors: ___

Factors of 20: ___ Factors of 30: ___ Common factors: ___

Factors of 24: ___ Factors of 36: ___ Common factors: ___

32

How Many Factors?

Circle how many factors each number has.

How many factors does 16 have?

3
4
5

How many factors does 7 have?

1
2
3

How many factors does 12 have?

4
6
8

How many factors does 1 have?

0
1
2
33

Factor and Multiple Word Problems (A)

Solve each problem.

Eggs come in boxes of 6. Can you buy exactly 50 eggs? Why or why not?

Draw here

I am thinking of a number that is a factor of both 18 and 24. What could it be? List all possibilities.

Draw here
34

Factor and Multiple Word Problems (B)

Solve each problem. Show your reasoning.

Chairs are arranged in equal rows. There are 36 chairs. List all the ways you could arrange them in equal rows.

Draw here

Two bells ring every 4 minutes and every 6 minutes. They both ring at 9:00 AM. When will they next ring together?

Draw here
35

Mystery Number Puzzles

Use the clues to find each mystery number.

I am a multiple of 5. I am a factor of 60. I am greater than 10. What am I? ___

I am between 20 and 30. I am a multiple of both 3 and 4. What am I? ___

I am a two-digit number. I am a multiple of 7. My digits add up to 9. What am I? ___

36

Quick Factor Check (A)

Circle the correct answer.

Which is a factor of 20?

3
4
6

Which is NOT a factor of 18?

3
4
9

Which number has exactly 2 factors?

4
7
9

How many factors does 1 have?

0
1
2
37

Quick Factor Check (B)

Circle the correct answer.

Which is a factor of 36?

5
7
9

Which number is a multiple of 8?

18
24
36

Is 15 a prime number?

Yes
No

The factors of 10 are...

1, 2, 5, 10
1, 5, 10
2, 5, 10
38

List Factor Pairs (A)

List all factor pairs.

Factor pairs of 16: ___

Factor pairs of 24: ___

Factor pairs of 30: ___

Factor pairs of 42: ___

39

First 5 Multiples (A)

Write the first 5 multiples.

Multiples of 4: ___

Multiples of 7: ___

Multiples of 11: ___

Multiples of 13: ___

40

Sort: Factor of 36 or Not?

Sort each number.

1
2
5
6
8
9
12
18
Factor of 36
Not a factor
41

Match Numbers to Factor Counts

Draw a line.

7 (prime)
12
16
25
3 factors
6 factors
2 factors
5 factors
42

Factor Pair Bonds (A)

Find the missing factor in the pair.

40
5
?
54
9
?
48
12
?
63
7
?
72
8
?
100
25
?
43

Common Factors (A)

Find all common factors.

Common factors of 12 and 16: ___. HCF: ___

Common factors of 18 and 27: ___. HCF: ___

Common factors of 20 and 35: ___. HCF: ___

44

Common Multiples (A)

Find the LCM.

LCM of 6 and 8: ___

LCM of 4 and 10: ___

LCM of 3 and 7: ___

45

Divisibility Rules Quick Check

Circle TRUE or FALSE.

456 is divisible by 2

TRUE
FALSE

345 is divisible by 5

TRUE
FALSE

612 is divisible by 3

TRUE
FALSE

124 is divisible by 4

TRUE
FALSE
46

Sort: Divisible by 3, by 4, or Both?

Sort each number.

9
16
12
21
36
28
24
15
Divisible by 3 only
Divisible by 4 only
Divisible by both
47

Match Number to Factor Count

Draw a line.

12
7
16
25
30
2 factors (prime)
6 factors
4 factors (square)
5 factors (square)
8 factors
48

Division Fact Bonds (C)

If a × b = c, find the missing factor.

48
6
?
72
8
?
56
7
?
90
9
?
32
4
?
66
6
?
49

Multiples and Factors True/False

Circle TRUE or FALSE.

36 is a multiple of 9

TRUE
FALSE

9 is a factor of 36

TRUE
FALSE

15 is a factor of 5

TRUE
FALSE

All factors of a number are less than or equal to that number

TRUE
FALSE
50

Sort: Factor or Multiple?

Sort each relationship as factor or multiple.

7 and 49 (7 is a ___ of 49)
63 and 7 (63 is a ___ of 7)
5 and 100 (5 is a ___ of 100)
100 and 5 (100 is a ___ of 5)
Factor
Multiple
51

Factor Ladders

Use a factor ladder to find prime factors.

Factor ladder for 48: Start by dividing by 2 repeatedly. Write the prime factorisation: ___

Factor ladder for 90: ___

What is the HCF of 48 and 90? Use the prime factors:

TipExtension: Prime factorisation using factor ladders and factor trees is enrichment content beyond the core Year 5 curriculum. Great for students who enjoy number puzzles.
52

Multiples in Problem Solving

Use multiples to solve.

A school library adds 8 new books every Monday. After 6 Mondays: ___ books added. If it started with 120, total: ___

Chairs are arranged in rows of 9. For 108 students, how many rows? ___

What is the smallest number that is a multiple of 4, 6 and 10? ___

53

Multiple Sequences

Continue each sequence of multiples.

6
12
18
24
?
?
7
14
21
28
?
?
11
22
33
44
?
?
54

Student Scores: Multiples of 6

Score = multiple of 6 earned in game. Each icon = 6 points.

Round 1
Round 2
Round 3
Round 4
1

Total score in points?

2

Which round had the highest score?

3

Average score per round?

4

How many more in Round 2 vs Round 3?

55

Factors of Numbers 1–12

Tally how many factors each number has.

ItemTallyTotal
2 factors (prime)
3 factors (square prime)
4 factors
6 or more factors
56

Compare Factor Counts

Tick which number has more factors.

12 (6 factors) vs 9 (3 factors) — which has more?

vs

24 (8 factors) vs 16 (5 factors) — which has more?

vs
57

Explain Divisibility

Explain the divisibility rules in your own words.

Divisibility rule for 4: ___

Is 2,316 divisible by 4? Show your reasoning:

Create your own 4-digit number that is divisible by both 3 and 4: ___. Show it works:

58

Factor Pairs of 36

Match each number to its partner to make a factor pair of 36.

1
2
3
4
6
9
18
12
36
6
59

Factor Pairs that Multiply to 60

Fill in the missing factor.

60
4
?
60
5
?
60
6
?
60
10
?
60

Is it a Multiple? (B)

Circle YES or NO.

Is 54 a multiple of 6?

YES
NO

Is 85 a multiple of 9?

YES
NO

Is 96 a multiple of 8?

YES
NO

Is 112 a multiple of 7?

YES
NO
61

Classify Numbers: Prime, Composite, or Square

Write each number in the correct column.

4
7
9
11
25
15
36
13
Prime
Composite
Perfect Square
62

LCM in Real Life

Use LCM to solve these problems.

A bus leaves every 8 minutes, a train every 12 minutes. Both leave at 9:00 am. When do they next leave together? ___

A lighthouse flashes every 6 seconds, another every 10 seconds. They flash together at 12:00:00. When next? ___

TipExtension: Lowest Common Multiple (LCM) and Highest Common Factor (HCF) are extension topics beyond the core Year 5 curriculum. These activities challenge students who are ready for deeper number work.
63

HCF Applications

Use HCF to solve.

You have 24 red beads and 36 blue beads. What is the largest equal group size with no beads left over? ___

A rectangular floor is 48 cm by 72 cm. What is the largest square tile that fits exactly? ___

TipExtension: HCF applications are enrichment content. Skip or revisit once core multiplication and division facts are secure.
64

Multiples and Patterns (B)

Find the pattern and continue.

3
6
12
24
?
?
128
64
32
?
?
1
4
9
16
?
?
65

Venn Diagram: Multiples

Sort numbers into the Venn diagram.

Draw two overlapping circles: 'Multiples of 3' and 'Multiples of 4'. Place 12, 8, 9, 24, 15, 16, 6, 32 in correct sections.

Draw here

Which numbers belong in the overlap? What do they have in common?

66

Factor or Multiple? (B)

Decide if the bold number is a factor OR multiple of the other.

7 is a ___ of 49

factor
multiple

63 is a ___ of 7

factor
multiple

6 is a ___ of 2

factor
multiple

2 is a ___ of 6

factor
multiple
67

Which Has More Factors?

Circle the number with more factors.

18 (6 factors) vs 20 (6 factors) — which has more?

vs

6 (4 factors) vs 36 (9 factors) — which has more?

vs
68

Factor Count Survey

Tally how many numbers 1–20 have exactly that many factors.

ItemTallyTotal
2 factors
3–4 factors
5–6 factors
More than 6
69

Design a Number Puzzle

Use factors and multiples to create a puzzle.

I am thinking of a number. It has exactly 4 factors. It is a multiple of 5. It is less than 30. What am I? ___

Write your own 'I am thinking of a number' puzzle using factors and multiples:

Draw here
70

Factors of 1–10

Each icon = 1 factor. Count factors for each number.

1
2
4
6
8
10
1

Which numbers are prime (2 factors)?

2

Which number has the most factors?

3

How many total factors do 1–10 have?

4

Which numbers are perfect squares?

71

Home Activity: Factor Pairs Game

Play a factor pairs game at home!

  • 1Pick a number between 20 and 50. Find all its factor pairs as fast as you can. Time yourself!
  • 2Write the multiples of 7 up to 70. Highlight any that are also multiples of 3.
  • 3Use egg cartons, blocks or counters to show that 24 can be arranged as 4×6, 3×8, 2×12 and 1×24.
  • 4Challenge a family member: give them a number and see who can find all the factors first.
72

Match Factor Pairs (C)

Draw a line to match each number to a factor pair.

48
60
72
100
6 × 10
8 × 9
5 × 12
6 × 8
73

Match Factor Pairs (D)

Match each number to a factor pair.

84
90
96
120
10 × 9
6 × 14
8 × 12
10 × 12
74

Is It a Factor? (C)

Circle the number that IS a factor of the given number.

Which is a factor of 60?

7
11
12

Which is a factor of 48?

5
8
11

Which is a factor of 84?

5
6
11

Which is a factor of 100?

3
7
25
75

Is It a Factor? (D)

Circle the number that IS a factor.

Which is a factor of 72?

5
9
11

Which is a factor of 96?

7
8
11

Which is a factor of 120?

7
11
15

Which is a factor of 64?

3
6
16
76

Factor Pairs of 60

60 can be split into two factors. Find the missing factor.

60
1
?
60
2
?
60
3
?
60
4
?
60
5
?
60
6
?
77

Factor Pairs of 100

100 can be split into two factors. Find the missing factor.

100
1
?
100
2
?
100
4
?
100
5
?
100
10
?
100
20
?
78

Sort: Multiple of 4, Multiple of 6, or Both?

Sort each number.

8
18
12
20
24
30
Multiple of 4 only
Multiple of 6 only
Multiple of both
79

Sort: Prime or Composite?

Is each number prime (only 2 factors) or composite (more than 2 factors)?

13
15
17
21
23
25
29
27
Prime
Composite
80

Prime or Composite? (A)

Circle Prime or Composite.

37

Prime
Composite

39

Prime
Composite

41

Prime
Composite

49

Prime
Composite
81

Prime or Composite? (B)

Circle the correct answer.

51 is...

Prime
Composite

53 is...

Prime
Composite

57 is...

Prime
Composite

61 is...

Prime
Composite
82

Multiples Sequences (C)

Fill in the missing multiples.

7
14
28
35
?
9
18
27
45
?
11
22
44
55
?
83

Multiples Sequences (D)

Fill in the missing multiples.

12
24
36
60
?
15
30
60
75
?
13
26
39
65
?
84

List All Factors (C)

List all factors of each number.

Factors of 48: ___

Factors of 60: ___

Factors of 72: ___

85

List All Factors (D)

List all factors.

Factors of 84: ___

Factors of 96: ___

Factors of 100: ___

86

Highest Common Factor (A)

Find the highest common factor (HCF) of each pair.

HCF of 12 and 18: ___

HCF of 24 and 36: ___

HCF of 30 and 45: ___

HCF of 48 and 60: ___

87

Lowest Common Multiple (A)

Find the lowest common multiple (LCM) of each pair.

LCM of 4 and 6: ___

LCM of 3 and 8: ___

LCM of 5 and 6: ___

LCM of 4 and 9: ___

88

Prime Factorisation (A)

Write each number as a product of prime factors.

12 = ___ × ___ × ___

18 = ___ × ___ × ___

24 = ___ × ___ × ___ × ___

30 = ___ × ___ × ___

89

Prime Factorisation (B)

Write each number as a product of prime factors.

36 = ___

48 = ___

60 = ___

72 = ___

90

Divisibility Rules (C)

Circle TRUE or FALSE.

2460 is divisible by 4

TRUE
FALSE

5775 is divisible by 9

TRUE
FALSE

1234 is divisible by 2

TRUE
FALSE

9999 is divisible by 3

TRUE
FALSE
91

Divisibility Rules (D)

Circle the correct answer.

Which rule? 3210 is divisible by 10 because...

ends in 0
digit sum divisible by 3
last two digits divisible by 4

Is 4512 divisible by 4?

Yes
No

Is 7890 divisible by 9?

Yes
No

Is 135 divisible by both 3 and 5?

Yes
No
92

Match Numbers to Their HCF

Match each pair to its HCF.

12 and 18
20 and 30
15 and 25
24 and 36
5
12
6
10
93

Match Numbers to Their LCM

Match each pair to its LCM.

4 and 6
3 and 5
6 and 8
5 and 7
35
24
12
15
94

Factors Graph

This graph shows how many factors each number has.

12 (6 factors)
15 (4 factors)
16 (5 factors)
18 (6 factors)
1

Which number has the most factors?

2

Which number has the fewest factors?

3

Why does 16 have 5 factors?

4

Find a number with exactly 3 factors.

95

Prime Numbers Tally

Count how many prime numbers fall in each range.

ItemTallyTotal
1-10
11-20
21-30
31-40
96

Factor and Multiple Word Problems (C)

Solve each problem.

A farmer has 84 apples. She wants to pack them in equal bags. List all possible bag sizes.

Tiles come in packs of 8 and 12. What is the smallest number of tiles you can buy to have equal packs of both?

97

Factor and Multiple Word Problems (D)

Solve and explain.

Two buses leave a station together. Bus A leaves every 15 minutes. Bus B every 20 minutes. When do they next leave together?

I have fewer than 50 stickers. I can share them equally among 4, 6 or 12 children. What number(s) could I have?

98

Highest Common Factor (B)

Find the HCF.

HCF of 36 and 48: ___

HCF of 45 and 60: ___

HCF of 56 and 84: ___

HCF of 72 and 96: ___

99

Lowest Common Multiple (B)

Find the LCM.

LCM of 6 and 9: ___

LCM of 8 and 12: ___

LCM of 10 and 15: ___

LCM of 12 and 18: ___

100

Arrays for Multiplication (A)

Each row shows an array. Count the total objects.

?
?
?
?
101

Compare Multiples (A)

Which group has more objects?

6th multiple of 6 vs 6th multiple of 4: which is bigger?

vs

5th multiple of 5 vs 3rd multiple of 7: which is bigger?

vs
102

Sort Numbers: Divisible by 2, 3 or Both?

Sort each number.

10
9
12
14
15
18
Divisible by 2 only
Divisible by 3 only
Divisible by both 2 and 3
103

Factor or Multiple? (A)

Is the first number a factor or multiple of the second?

3 and 12: 3 is a ___ of 12

factor
multiple

15 and 5: 15 is a ___ of 5

factor
multiple

6 and 36: 6 is a ___ of 36

factor
multiple

40 and 8: 40 is a ___ of 8

factor
multiple
104

Create Your Own Factor Problems

Write and solve your own factor and multiple problems.

Write a number between 50 and 100 with exactly 6 factors. What is it? List the factors.

Write a problem involving LCM. Solve it.

Draw here

What to do next

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