# Identify Common Factors, Multiples and Prime Numbers

In this worksheet, students will use their knowledge of common factors, multiples and prime numbers to answer a variety of questions.

Key stage:  KS 2

Curriculum topic:   Number: Addition, Subtraction, Multiplication and Division

Curriculum subtopic:   Identify Common Factors, Multiples and Prime Numbers

Difficulty level:

### QUESTION 1 of 10

In this activity, you will need to have an understanding of common factors, multiples and prime numbers.

Common factors:

Common factors or factors are numbers that we multiply together to make another number.

When we find the factors of two or more numbers and then find some factors are the same (common) then they are called common factors.

Example: 12 and 16

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

Factors of 16: 1, 2, 4, 8 and 16

So the common factors of 12 and 16 are 1, 2 and 4.

The highest common factor of two numbers is the largest whole number which is a factor of both.

The highest common factor of 12 and 16 is 4.

Multiples:

On multiplying a number, by counting numbers, gives us it's multiples.

A common multiple is a whole number that is a shared multiple of sets of numbers.

Example:

Multiples of 3 and 4;

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

The common multiples of 3 and 4 are: 12 and 24.

Prime Numbers:

A prime number is a number only divisible by itself and 1.

Example: prime numbers between 10 and 30.

Answer: 11, 13, 17, 19, 23, 29.

Want to understand this further and learn how this links to other topics in maths?

Why not watch this video?

From the options available, can you choose the smallest number that is a multiple of both 2 and 7?

72

78

79

82

83

84

88

90

Choose the number that is not a multiple of 2, 3 or 5.

71

78

82

91

97

100

Can you correctly identify which number is a common multiple of 3 and 5?

Can you identify the common multiples of 3 and 8 that are less than 50 by writing 'yes' or 'no' in the boxes provided?

 22 24 33 38 41 48 Common Multiple of 3 and 8

Can you find the prime number in the list given?

How many common factors are there for the numbers 20 and 30?

Can you write a number that is a common multiple of 4 and 6, ends in 2 and is less than 50?

Can you find the 2 prime numbers from the options given below?

203

207

211

219

223

225

Can you record the highest common factor of 16 and 48?

Can you choose the common factors for 21, 36 and 42?

 1 2 3 7 14 36 Common Factors
• Question 1

From the options available, can you choose the smallest number that is a multiple of both 2 and 7?

CORRECT ANSWER
84
EDDIE SAYS
The smallest number that is a multiple of both 2 and 7 is 84 as it divides by both 2 and 7 equally, without leaving a remainder. 84 ÷ 2 = 42 84 ÷ 7= 12 Is this beginning to make more sense?
• Question 2

Choose the number that is not a multiple of 2, 3 or 5.

CORRECT ANSWER
97
EDDIE SAYS
How did you get on? 97 is the correct number as it's not a multiple of 2, 3 or 5. This because it has a remainder when divided by 2, 3 or 5. 97 ÷ 2 = 48.5 97 ÷ 3 = 32.3 97 ÷ 5 = 19.4
• Question 3

Can you correctly identify which number is a common multiple of 3 and 5?

CORRECT ANSWER
EDDIE SAYS
Did you find it? The common multiple of 3 and 5 is 30. Although, as we can see from the list below, the lowest common multiple of the 2 numbers is 15 but that wasn't an option! Well done if you noticed that. Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30... Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50...
• Question 4

Can you identify the common multiples of 3 and 8 that are less than 50 by writing 'yes' or 'no' in the boxes provided?

CORRECT ANSWER
 22 24 33 38 41 48 Common Multiple of 3 and 8
EDDIE SAYS
This question requires us to use our knowledge of the times tables to find the common multiples for 3 and 8. By working through each times table, we can see that the common multiples available were 24 and 48. 3 x 8 = 24 3 x 16 = 48 6 x 8 = 48
• Question 5

Can you find the prime number in the list given?

CORRECT ANSWER
EDDIE SAYS
The prime number listed is 29 as it is the only number available divisible only by itself and 1. All of the other options are divisible by additional numbers. E.g. 68 ÷ 2 = 34
• Question 6

How many common factors are there for the numbers 20 and 30?

CORRECT ANSWER
4
Four
EDDIE SAYS
There were a few to find here. To find the common factors of 20 and 30, we have to find the factors of each number first. Factors of 20 are 1, 2, 4, 5, 10, 20. Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The factors that 20 and 30 have in common are 1, 2, 5, 10.
• Question 7

Can you write a number that is a common multiple of 4 and 6, ends in 2 and is less than 50?

CORRECT ANSWER
12
EDDIE SAYS
Hopefully, you realised that you needed to initially find the multiples of each number, up to 50: Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48... Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48... Using these lists, we could then look for a common multiple, ending in 2, therefore giving us the answer of 12! Examiners love questions like this which add an extra step onto the process. Great work if you got this right, no worries if not.
• Question 8

Can you find the 2 prime numbers from the options given below?

CORRECT ANSWER
211
223
EDDIE SAYS
Did you find the 2 prime numbers? The correct answers were 211 and 223 as they were the only numbers that can be divided solely by themselves and 1. All of the other numbers can be divided by other numbers, e.g. 215 ÷ 5 = 43.
• Question 9

Can you record the highest common factor of 16 and 48?

CORRECT ANSWER
16
EDDIE SAYS
The highest common factor of 16 and 48 is 16. We can clearly find the highest common factor by creating a list of all of the factors of each number and then comparing. Factors of 16: 1, 2, 4, 8 and 16. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
• Question 10

Can you choose the common factors for 21, 36 and 42?

CORRECT ANSWER
 1 2 3 7 14 36 Common Factors
EDDIE SAYS
I bet you're getting the hang of this now! As before, to find the common factors, it is easiest to first find the factors of each number. Factors of 21: 1, 3, 7, 21 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 From looking carefully at each list, we can see the common factors are 1 and 3. In fact, 3 is also the highest common factor for 21, 36 and 42. Amazing job! That's another activity ticked off. Phew.
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