2C Divisibility tests

Learning intentions for this section:

• To know the meaning of the terms divisible, divisor, dividend, quotient and remainder

• To understand that divisibility tests can be used to check if a number is divisible by another number without performing the division

• To be able to test for divisibility by 2, 3, 4, 5, 6, 8, 9 and 10

Past, present and future learning:

• The concepts in this section may be new to students

• This section prepares students for future work with fractions

• These concepts are assumed knowledge for future learning beyond Stage 4

It is useful to know whether a large number is exactly divisible by another number. Although we can always carry out the division algorithm, this can be a difficult and tedious process for large numbers. There are simple divisibility tests for each of the single-digit numbers, with the exception of 7. These divisibility tests determine whether or not the number is divisible by the chosen divisor.

Lesson starter: Five questions in 5 minutes

In small groups, attempt to solve the following five questions in 5 minutes.

1 Some numbers greater than 1 are only divisible by 1 and themselves. What are these numbers called?

2 Is 21541837 divisible by 3?

3 What two-digit number is the ‘most divisible’ (i.e. has the most factors)?

4 Find the smallest number that is divisible by 1, 2, 3, 4, 5 and 6.

5 Find a number that is divisible by 1, 2, 3, 4, 5, 6, 7 and 8.

Key Ideas

■ A number is said to be divisible by another number if there is no remainder after the division has occurred. For example, 20 is divisible by 4 because 20 ÷ 4 = 5 with no remainder.

■ If the divisor divides into the dividend exactly, then the divisor is said to be a factor of that number.

■ Division notation

The first number is called the dividend and the second number is called the divisor.

Example: 27 ÷ 4 = 6 remainder 3