Divisibility Rules
Quick Tests to Check If Numbers Divide Evenly
What Are Divisibility Rules?
Divisibility rules (also called divisibility tests or divisibility criteria) are quick shortcuts that help us determine if one number divides evenly into another without performing long division.
Key Idea
When a number divides evenly, there is no remainder. We write this as: a ÷ b = whole number or say "a is divisible by b".
Divisible
24 ÷ 6 = 4 (no remainder)
We say: "24 is divisible by 6"
Not Divisible
25 ÷ 6 = 4 R1 (remainder 1)
We say: "25 is NOT divisible by 6"
Why Are Divisibility Rules Useful?
- Save time — avoid long division
- Simplify fractions — find common factors
- Find factors quickly
- Mental math — check calculations in your head
- Prime numbers — essential for finding primes
- Verify answers — double-check your work