Divisibility Rules — Quick Checks (Grades 4–5)
Divisibility rules let you tell whether one number divides another without doing the full division. A number is divisible by 2 if it's even (ends in 0,2,4,6,8); by 5 if it ends in 0 or 5; by 10 if it ends in 0; by 3 if the sum of its digits is divisible by 3; by 9 if the digit sum is divisible by 9. These shortcuts make factoring and simplifying much faster.
Understanding divisibility rules
Divisibility rules let you tell whether one number divides another without doing the full division. A number is divisible by 2 if it's even (ends in 0,2,4,6,8); by 5 if it ends in 0 or 5; by 10 if it ends in 0; by 3 if the sum of its digits is divisible by 3; by 9 if the digit sum is divisible by 9. These shortcuts make factoring and simplifying much faster.
Key Idea
Divisibility rules let you tell whether one number divides another without doing the full division. A number is divisible by 2 if it's even (ends in 0,2,4,6,8); by 5 if it ends in 0 or 5; by 10 if it ends in 0; by 3 if the sum of its digits is divisible by 3; by 9 if the digit sum is divisible by 9. These shortcuts make factoring and simplifying much faster.
Seeing it in action
Worked example
Is 126 divisible by 3?
Add the digits: 1 + 2 + 6 = 9. 9 is divisible by 3. → Yes (126 = 3 × 42).
Digit sum 9 shows 126 is divisible by 3.
Try a few
Is 84 divisible by 2?
it's even.
Is 45 divisible by 9?
4+5 = 9.
Is 130 divisible by 5?
ends in 0.
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Put the reasoning on paper.
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