Multiplication and division
Tests of divisibility
A divisibility test is a quick way to check whether one number divides exactly into another, without doing the whole division.
The tests
• Divisible by 2: the ones digit is even (0, 2, 4, 6 or 8). • Divisible by 4: the number made by the last two digits divides by 4. • Divisible by 8: half the number is divisible by 4 (and every multiple of 8 is also a multiple of 4).
Worked examples
Test for 2: is 146 divisible by 2?
- Look at the ones digit: 6.
- 6 is even.
Answer: Yes — 146 is divisible by 2.
Test for 4: is 632 divisible by 4?
- Look at the last two digits: 32.
- 32 ÷ 4 = 8, a whole number.
Answer: Yes — 632 is divisible by 4.
Test for 8: is 48 divisible by 8?
- Check if 8 divides the number exactly.
- 8 × 6 = 48.
Answer: Yes — 48 is divisible by 8.
Where you see this in real life
- Checking if a group of items can be shared into equal teams of 4 or 8.
- Packing objects into boxes without any left over.
- Quickly spotting even numbers (divisible by 2).
Key words
- Divisible
- Can be divided by a number with nothing left over.
- Divisibility test
- A quick rule to check if a number divides exactly, without doing the division.
- Multiple
- The result of multiplying a number by a whole number. The first multiples of 4 are 4, 8, 12, 16, …