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Number seven spelt out in child's blocks

7 is a prime number. It can only be divided exactly by itself and by 1.

Properties of Numbers 2 (Difficult)

This 11 Plus Maths quiz explores fascinating relationships between numbers, including special pairs, sequences, and how factors can reveal surprising mathematical connections.

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Fascinating Fact:

The numbers 220 and 284 are called amicable numbers because each number’s factors add up to the other, a mathematical friendship discovered by the ancient Greeks.

In 11 Plus Maths, pupils study how numbers relate to one another through factors, multiples, and divisibility. These ideas form the foundation for patterns, algebra, and reasoning across many areas of maths.

Key Terms

Factor: A number that divides exactly into another number with no remainder.
Multiple: A number made by multiplying one number by another, such as 4 × 3 = 12.
Divisibility: A rule that helps decide whether one number divides evenly into another.

For more insight, read our guide for parents about 11 Plus sample questions.

Frequently Asked Questions (Click to see answers)

What are examples of special relationships between numbers?

Some pairs of numbers share unique connections, such as twin primes that differ by two, or perfect numbers where all factors add up to the number itself.

How do factors and multiples help in problem solving?

Recognising factors and multiples helps simplify fractions, find common denominators, and solve ratio and proportion problems more efficiently in exams.

Why do mathematicians study number patterns?

Number patterns reveal how mathematical systems behave. They help predict sequences, understand symmetry, and even develop new ideas in coding and cryptography.

Try These Related Quizzes

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

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 .

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

A prime number

An odd number

An even number

Either an odd or an even number

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

3 .

There is only one prime number that ends in a 5. Can you name it?

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

4 .

What is a factor?

A number which is the result of multiplying a number by itself

A number that can only be divided exactly by itself or by 1

A number that may be divided exactly by another number

A number that divides exactly into another number

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

5 .

Which of the following statements is false?

All prime numbers are odd

Numbers which are not prime are called composite numbers

0 and 1 are not prime numbers

7 is a prime number

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

6 .

What is the smallest square number?

-2

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

7 .

Which number is the odd man out: 16, 36, 64, 110?

110

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

8 .

Which number is the odd man out: 19, 27, 31, 43?

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

9 .

How many square numbers are there between 1 and 100?

Here they are:
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100

10 .

Which of the following statements is wrong?

13 is a prime number

49 is a square number

The square root of 25 is 5

Square numbers can also be prime numbers

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

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)