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 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

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


They are: 1, 2, 3, 4, 6 and 12
The factors of a number are the numbers that divide exactly into it 
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 

Negative numbers cannot be squares because if you multiply two negatives the result is a positive:
2 x 2 = 4 
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


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

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 

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

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