Divisibility Tests

Why use Divisibility Tests?

It’s easy to see that 10 divides 20. But does 10 divide 8560? Divisibility tests allow us to check large numbers without doing long division.

The Rules

Divisibility by 10

• Rule: The number must end in 0.
• Examples: 20, 500, 8560 (Yes). 125 (No).

Divisibility by 5

• Rule: The number must end in 0 or 5.
• Examples: 15, 75, 100 (Yes). 43 (No).

Divisibility by 2

• Rule: The number must be even (ends in 0, 2, 4, 6, 8).
• Examples: 12, 38, 556 (Yes). 19 (No).

Divisibility by 4

• Rule: Look at the last two digits. If the number formed by the last two digits is divisible by 4, the whole number is.
• Example: 8536
  • Last two digits: 36.
  • Is 36 divisible by 4? Yes ($4 \times 9 = 36$).
  • So, 8536 is divisible by 4.
• Example: 1714
  • Last two digits: 14.
  • Is 14 divisible by 4? No.
  • So, 1714 is not divisible by 4.

Divisibility by 8

• Rule: Look at the last three digits. If the number formed by them is divisible by 8, the whole number is.
• Example: 3128
  • Last three digits: 128.
  • $128 \div 8 = 16$.
  • So, 3128 is divisible by 8.