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Properties of Numbers Illustration | Factor

A factor is a number that is multiplied to get another. E.g. 2 and 5 are factors of 10.

Properties of Numbers 3 (Difficult)

This 11 Plus Maths quiz explores triangular numbers and how patterns built from simple shapes reveal deeper mathematical relationships and sequences.

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Fascinating Fact:

A triangular number describes a pattern of dots that form perfect triangles, and the 100th triangular number is 5,050.

In 11 Plus Maths, pupils study how numbers can form patterns and shapes, such as squares, cubes, and triangles. Recognising these patterns improves logical thinking and supports future topics in algebra and geometry.

Key Terms

Triangular Number: A number that can be shown as a triangle made of dots, found by adding consecutive numbers together.
Sequence: A set of numbers arranged in a specific order or pattern.
Formula: A rule written in symbols to describe a mathematical relationship or calculation.

Learn more about 11 Plus courses and materials in our guide for parents.

Frequently Asked Questions (Click to see answers)

How do you find a triangular number?

You find a triangular number by adding consecutive whole numbers together. For example, 1 + 2 + 3 + 4 = 10, so 10 is the 4th triangular number.

What is the formula for triangular numbers?

The formula is n(n + 1) ÷ 2, where n is the position in the sequence. For example, if n = 5, the 5th triangular number is 15.

Where are triangular numbers used in real life?

Triangular numbers appear in arrangements such as bowling pins, stacking cannonballs, and even in computer science when designing data structures and networks.

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

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 .

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

3 .

How many factors does the number 12 have?

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

4 .

Which of the following numbers is a factor of 279?

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

5 .

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

6 .

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

7 .

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

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

8 .

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

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

9 .

Which number is the odd man out: 27, 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

10 .

Which of the following numbers is a multiple of 18?

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

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