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Properties of Numbers Illustration | property
This quiz investigates the properties of numbers.

Properties of Numbers 3 (Medium)

This 11 Plus Maths quiz explores prime numbers and how they form the foundation for all other numbers in mathematics.

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Fascinating Fact:

Every whole number greater than one is either a prime or can be made by multiplying primes, making prime numbers the building blocks of all maths.

In 11 Plus Maths, pupils study prime, composite, and square numbers. These ideas show how numbers are related and help pupils understand patterns, factors, and divisibility.

Key Terms

  • Prime Number: A number that can only be divided exactly by one and itself.
  • Composite Number: A number that has more than two factors, such as 6 or 9.
  • Factorisation: Breaking down a number into the prime numbers that multiply to make it.

Read more about the 11 Plus in our guide for parents on 11 Plus courses and materials.

Frequently Asked Questions (Click to see answers)

What are prime numbers in maths?

Prime numbers are numbers that can only be divided exactly by one and themselves. Examples include 2, 3, 5, 7, and 11. They cannot be split evenly by any other number.

How can you tell if a number is prime?

A number is prime if it has only two factors: one and itself. To test this, check whether it divides evenly by any smaller number apart from one.

Why are prime numbers called the building blocks of maths?

Prime numbers are called building blocks because every other whole number can be made by multiplying primes together. This process is called prime factorisation.

Try These Related Quizzes

1 .
Which of these numbers is a multiple of 24?
4
6
12
48
If a number is a multiple of another number, then it is divisible by the other number exactly a certain number of times.
4, 6 and 12 go into 24 exactly:
4 x 6 = 24, 6 x 4 = 24 and 12 x 2 = 24 - but that means 24 is a multiple of those numbers. Only 48 is a multiple of 24 because 24 x 2 = 48
2 .
Which words do not describe the numbers 8, 16, 24 and 32?
Even numbers
Prime numbers
Whole numbers
Multiples of eight
They are all whole even numbers and multiples of 8. Prime numbers are not divisible by any number except one and themselves, so the only even prime number is 2
3 .
Which of the following statements is true?
7 is a prime number
4 is a multiple of 8
30 is a square number
An odd number plus an even number equals an even number
30 is not a square number: 5 x 5 = 25, 6 x 6 = 36
4 is not a multiple of 8, though 8 is a multiple of 4: 4 x 2 = 8
An odd number plus an even number equals an odd number.
7 is a prime number because it is only divisible by 1 and by 7: 7 x 1 = 7, 1 x 7 = 7
4 .
Which of the following is a square number?
66
88
100
111
A square number is formed by multiplying another number with itself : 10 x 10 = 100
5 .
What do you always get when you add a negative whole number and a negative whole number?
A positive number
A negative number
Either a positive or negative number
Either a positive number or negative number or zero
Negative plus negative equals negative:
For example: -2 + -2 = -4
6 .
If a number is divisible by 8, what must the final digit of the number be?
8
6 or 8
2, 4, 6 or 8
0, 2, 4, 6 or 8
Numbers in the 8 times table all end with an even number or with 0
7 .
If a number is divisible by 9, what must the final digit of the number be?
9
6, 7, 8 or 9
1, 3, 5, 7 or 9
0, 1, 2, 3, 4, 5, 6, 7, 8 or 9
As 9 is an odd number, its multiples can end with any number. Go through your 9 times table and you’ll see this is true
8 .
What happens to an odd number if you multiply it by 3?
It remains an odd number
It becomes an even number
It could be either odd or even
There are no rules
When we multiply two odd numbers (3 is an odd number) the result is always an odd number – try it yourself to see
9 .
What happens to an even number if you multiply it by 6?
It becomes an odd number
It remains an even number
It could be either odd or even
There are no rules
When we multiply two even numbers (6 is an even number) the result is always an even number – try it yourself to see
10 .
Which of the following statements is wrong?
If a number is divisible by 6, it is an even number
If a number is divisible by 14, it is divisible by 7
If a number is divisible by 6, it is divisible by 12
If a number is a multiple of 12, it is divisible by both 3 and 4
3 x 6 = 18 BUT 18 is NOT divisible by 12. If you want to show that a statement is not always true, find one example that shows it is wrong - like we did here
Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)
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