Special numbers
Tests of divisibility
A divisibility rule is a quick way to tell if one number divides exactly into another, without doing the whole calculation. Here you find numbers divisible by 2, 5, 10, 25, 50 and 100.
What divisibility means
A number is divisible by another if it divides exactly, with no remainder. For example, 20 is divisible by 5 because 20 ÷ 5 = 4 with nothing left over. Divisibility rules let you check quickly, which helps when you are calculating or checking a code.
Rules for 2, 5 and 10
• Divisible by 2: the number is even — it ends in 0, 2, 4, 6 or 8. • Divisible by 5: the number ends in 0 or 5. • Divisible by 10: the number ends in 0. For example, 284 is divisible by 2, 300 is divisible by 5 and 10, and 74 is not divisible by 5.
Rules for 25, 50 and 100
• Divisible by 100: the number ends in two zeros (00). • Divisible by 50: the number ends in 00 or 50. • Divisible by 25: the last two digits are 00, 25, 50 or 75. For example, 700 is divisible by 100, 1250 is a multiple of 50, and 525 is a multiple of 25.
Using factors to help
If a number is divisible by 100, it is also divisible by every factor of 100 — that is 2, 5, 10, 25 and 50. In the same way, if a number is divisible by 50 it is also divisible by 2, 5, 10 and 25, and if it is divisible by 25 it is also divisible by 5.
Worked examples
Testing for divisibility by 2
- Is 284 divisible by 2?
- Look at the last digit: 4 is even, so the number is even.
Answer: Yes, 284 is divisible by 2.
Testing for divisibility by 5
- Is 300 divisible by 5?
- The number ends in 0, which is allowed for divisibility by 5.
Answer: Yes, 300 is divisible by 5.
Divisible by 100 and its factors
- 700 ends in 00, so it is divisible by 100.
- So it is also divisible by every factor of 100: 2, 5 and 10.
Answer: 700 is divisible by 100, 2, 5 and 10.
Where you see this in real life
- Checking whether a product barcode is valid.
- Sharing an amount equally with no leftovers.
- Counting money in 5s, 10s or 25s.
Key words
- Divisible
- One number divides exactly into another with no remainder.
- Divisibility rule
- A quick test to see if a number divides exactly, such as 'even numbers are divisible by 2'.
- Factor
- A whole number that divides another number exactly.
- Multiple
- The result of multiplying a number by a whole number.
- Even number
- A number that ends in 0, 2, 4, 6 or 8 and is divisible by 2.