Welcome to the third of our Difficult Eleven Plus maths quizzes on Properties of Numbers. Do you know about prime numbers, factors, multiples and square numbers? Hopefully, you will have played our previous quizzes and be quite familiar with them. This quiz gives you more opportunity to practise with them.

Many people mistakenly believe that 1 is a prime number because prime numbers are divisible by themselves and by 1. This does apply to the number 1, but it is not a prime number. Why? Well, prime numbers are divisible by two numbers: 1 and themselves. 1 is not a prime number because it is only divisible by one number – the number 1.

The more often you play these quizzes, the better you will become at maths. Even when you have mastered a topic, it’s a good idea to come back and play the quizzes again. We can all get a little rusty over time!

1.

A square number is the result of multiplying a number by itself. The square of an odd number will always be…?

A prime number

An odd number

An even number

Either an odd or an even number

1 x 1 = 1 (an odd number), 3 x 3 = 9 (an odd number), 5 x 5 = 25 (an odd number)… if you want to test the idea further, then try working out the squares of some other odd numbers

2.

The square of a negative number will be …?

… a positive number

… a negative number

… either a positive or a negative number

… neither a positive nor a negative number

Negative numbers cannot be squares because if you multiply two negatives the result is a positive:

-2 x -2 = 4

-2 x -2 = 4

3.

Which of the following numbers is a multiple of 18?

3

6

9

36

Multiples are the numbers in another number’s times table: 18 x 2 = 36

4.

Which number is the odd man out: 27, 39, 57, 71, 87

39

57

71

87

They are all odd and they are all divisible by 3, except for 71, which is a prime number: a prime number is a positive whole number that is only divisible by 1 and itself

5.

How many prime numbers are there between 30 and 60 inclusive?

5

6

7

8

They are 31, 37, 41, 43, 47, 53, 59. Well done if you worked them out!

6.

How many factors does the number 12 have?

4

5

6

An infinite amount

They are: 1, 2, 3, 4, 6 and 12

The factors of a number are the numbers that divide exactly into it

The factors of a number are the numbers that divide exactly into it

7.

How many square numbers are there between 1 and 100 inclusive?

7

8

9

10

The square of a number is the result when you multiply it by itself. 10 squared is 100 so that means there will be 10 square numbers between 1 and 100:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 = 49

8 x 8 = 64

9 x 9 = 81

10 x 10 = 100

11 x 11 = 121, but this is greater than 100 so does not count

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 = 49

8 x 8 = 64

9 x 9 = 81

10 x 10 = 100

11 x 11 = 121, but this is greater than 100 so does not count

8.

Which number is the odd man out: 1, 3, 5, 7, 11

1

3

7

11

They are all prime numbers except for 1. Prime numbers have two divisors, 1 and themselves. However, 1 only has one divisor (1 itself), so it is not prime

9.

Which of the following numbers is a factor of 279?

5

7

9

11

To work out whether a number is a factor of another, divide the larger number by the smaller. If there is no remainder, then it is a factor:

279 ÷ 9 = 31

279 ÷ 9 = 31

10.

Which of the following statements is false?

All prime numbers are odd

Square numbers can be odd or even

29 is a prime number

121 is a square number

There is one prime number that is even – the number 2. Every other prime number is odd