# Unit 2 Section 1 : Factors and Prime Numbers

A factor is a whole number which divides exactly into a whole number, leaving no remainder.

For example, 13 is a factor of 52 because 13 divides exactly into 52 (52 ÷ 13 = 4 leaving no remainder).
The complete list of factors of 52 is: 1, 2, 4, 13, 26, and 52 (all these divide exactly into 52).

A prime number has exactly two factors, 1 and itself.

For example, 13 is a prime number because the only factors of 13 are 1 and 13.
The number 8 is not prime because it has four factors: 1, 2, 4 and 8.

The number 1 is not a prime number because it only has one factor (itself).

## Practice Question 1

You are going to work out which of the whole numbers from 1 to 10 are prime.
You will start by working out the factors of each number - the prime numbers are the ones with exactly two factors.

Work out the factors of each number then click on the button marked to see whether you are correct.

 The factors of 1 are The factors of 2 are The factors of 3 are The factors of 4 are The factors of 5 are The factors of 6 are The factors of 7 are The factors of 8 are The factors of 9 are The factors of 10 are Which of the numbers 1 to 10 are prime numbers? ## Practice Question 2

Work out which of the following numbers are prime numbers : 18, 45, 79, 90 and 97.
 Is the number 18 prime? Is the number 45 prime? Is the number 79 prime? Is the number 90 prime? Is the number 97 prime? ## Practice Question 3

Work out the prime factors of the number 24.
To do this you need to find all the factors of 24, then check which ones are prime.

(a) What are the factors of 24? (b) What are the prime factors of 24? ## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

In this section you need to give a list of numbers for some of the answers.
The order doesn't matter, but separate the numbers with commas, like this: Question 1
List all the factors of the following numbers.

(a) 11  (b) 12  (c) 13  (d) 14  (e) 15  (f) 16  (g) 17  (h) 18  (i) 19  (j) 20  Which of the numbers 11 to 20 are prime numbers?  Question 2
Decide if each of the numbers below are prime or not prime.

(a) 33  (b) 35  (c) 37  (d) 39  (e) 41  Question 3
In this question you will be finding the prime factors of the number 72.

(a) Firstly, write down all the factors of 72.  (b) Now, write down the prime factors of 72.  Question 4
(a) Enter the prime factors of 40.  (b) Enter the prime factors of 70.  (c) List the prime factors which 40 and 70 have in common?  Question 5
A number has prime factors 2, 5 and 7.

Which is the smallest number that has these prime factors?  Question 6
The first 5 prime numbers are 2, 3, 5, 7 and 11.

What is the smallest number that has these five numbers as prime factors?  Question 7
Work out the first two prime numbers which are greater than 100.

The first prime number greater than 100 is:  The second prime number greater than 100 is:  Question 8
What is the first prime number that is greater than 200?  You have now completed Unit 2 Section 1
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