Multiples and factors,what you need to learn

f A times B equals to C, then A and B are factors of C,
whereas C is a multiple of both A and B.
What is factor and multiple?

"Factors" are the numbers we can multiply together
to get another number
Factors
Can a number can have many
factor?

A multiple is the result of multiplying a number by
an integer (not a fraction).
Multiple

If A times B equals to C, then A and B are factors of
C, whereas C is a multiple of both A and B.
What is factor and multiple?

Identify Multiples of…
• How do you know a number is a multiple of 2?
•
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The number is even – ends in 0, 2, 4, 6 or 8
The digital root is 3, 6 or 9 (add the digits until you get a single
digit)
The last 2 digits are in the 4 times table.
The last digit is 5 or 0.
The digital root is 3, 6 or 9 and the number is
even.
The digital root is 9.
The last digit is 0

Write out the first 10 multiples of the numbers
below, and then answer the questions:
4 20 12 25 8
1. What common multiples have you written for the numbers 8 and
12?
2. What common multiples have you written for the numbers 4 and
20?
3. What is the lowest common multiple of 20 and 25?

Answers
1. Common multiples for the numbers 8 and 12 are: 24, 48, 72
2. Common multiples for the numbers 4 and 20 are: 20 and 40
3. The lowest common multiple of 20 and 25 is 100.
1. 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
2. 20, 40, 60, 80, 100, 120, 140, 160, 180, 200
3. 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
4. 25, 50, 75, 100, 125, 150, 175, 200, 225, 250
5. 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

Answers
Day 2
1. A multiple of 3:
2. A multiple of 7:
3. A multiple of 8:
4. A multiple of 12:
5. A multiple of 6:
6. A multiple of 3 and 4:
7. A multiple of 5 and
12:
80 327 82 28 32
15 98 17 157 34
18 293 128 25 258
40 22 75 156 100
56 62 434 150 63
9 90 16 104 48
20 40 80 60 100

Factor Pairs
• Explain how you would find all the factor pairs
of 36 to make sure you have found them all.
• Compare your answer with a partner. Can you
improve your explanations?
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Start with 1 and the number itself - 36. Write
either end of the list.
1 36
Work through each number to see if it one of
a pair. In this case 2 × 18, 3 × 12, 4 × 9. 5 is
not a factor. 6 × 6. This is the last pair as the
numbers from 1 and from 36 have met at 6.
1 2 3 4 6 9 12 18 36

Common Factors
• Name one common factor of 28
and 54, explaining how you
know.
• Can you find the highest
common factor of 28 and 54?
Both numbers are even, so 2 is
a common factor.
The highest common factor is
2.
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Common Factors
know.
• Can you find the highest
common factor of 35 and 60?
Both numbers end in 5 or 0, so
5 is a common factor.
The highest common factor is
5.
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Common Factors
know.
• Write some numbers for which a
partner should find common
factors.
The digital root of 42 is 6 (4 + 2 = 6)
The digital root of 75 is 3 (7 + 5 = 12, 1 + 2 =3)
Both numbers have a digital root of 3, 6 or 9,
so 3 is a common factor. Note 6 is not a
common factor as 75 is odd.
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Draw a Venn diagram in your jotter.
Write any numbers between 1 and 50 that are factors of 36 and 48 in
the correct place on the diagram.
How does the Venn diagram help you identify the common factors of
36 and 48?
Factor of 36 Factor of 48

Answers
Factor of 36 Factor of 48
9
36
18
8
16
24
48
1
3 2
4 6
12

I am
Who Am I?
My factors are …
1
2
5
10
10

I am
Who Am I?
My factors are …
1 2
3
4
6
12
12

I am
Who Am I?
My factors are …
1
15
3
5
15

I am
Who Am I?
My factors are …
3 2 6
9 18
18
1

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