This is the second quiz in the Difficult section of our Eleven Plus maths series on Properties of Numbers. In previous quizzes we learned about prime numbers and multiples. In this one, we continue to look at those, but also some others such as factors.
Just to remind you before we start:
Now you’ve refreshed your memory, it’s time for the quiz. Good luck!














3 x 3 = 9 (an odd number), 5 x 5 = 25 (an odd number), 7 x 7 = 49 (an odd number)… if you want to test the idea further, then try working out the squares of some other odd numbers

2 x 2 = 4 (an even number), 4 x 4 = 16 (an even number), 6 x 6 = 36 (an even number)… if you want to test the idea further, then try working out the squares of some other even numbers


Every number ending in 5 is divisible by 5. 5 itself is a prime number because it is only divisible by 1 and by 5

The factors of a number are the numbers that divide exactly into it, for example:
The number 24 has 8 factors: 1, 2, 3, 4, 6, 8, 12, 24 24 x 1 = 24, 12 x 2 = 24, 3 x 8 = 24 and 4 x 6 = 24 

There is only one prime number that is even – the number 2. All other even numbers can be divided by 2.
A composite number is any number greater than 1 which is not a prime number 
0 is not considered a square number because a square that measures 0 cm x 0 cm is not a square – in fact, it couldn’t exist!
Negative numbers cannot be squares because if you multiply two negatives the result is a positive 

They are all even numbers, but all of them except 110 are square numbers too

They are all odd numbers, but all of them except 27 are prime numbers too


Here they are:
1^{2} = 1 2^{2} = 4 3^{2} = 9 4^{2} = 16 5^{2} = 25 6^{2} = 36 7^{2} = 49 8^{2} = 64 9^{2} = 81 10^{2} = 100 
Square numbers (except 1) have at least 3 factors – their square root, 1 and themselves. Prime numbers have only 2 factors – 1 and themselves.
1 is a square number but it is not a prime number 