Concept 4 of 8Foundation
Watch on YouTubeVideoDivisibility rules (shortcuts)
You don't always need to divide — these tests tell you instantly:
- by 2: last digit is even (0, 2, 4, 6, 8)
- by 3: digit-sum divisible by 3
- by 4: last 2 digits divisible by 4
- by 5: ends in 0 or 5
- by 6: divisible by 2 AND 3
- by 8: last 3 digits divisible by 8
- by 9: digit-sum divisible by 9
- by 10: ends in 0
- by 11: (alternating sum) is divisible by 11
Example
Is 2,934 divisible by 9?
Digit sum = 2+9+3+4 = 18 → 18 ÷ 9 = 2. Yes ✓.
Digit sum = 2+9+3+4 = 18 → 18 ÷ 9 = 2. Yes ✓.
💡 Tip:These tests save loads of time in olympiads.
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5 questions to check what you just read.
0 / 5
- Q1.Which is divisible by 3? (hint: digit sum)
- Q2.Divisible by 4?
- Q3.Which is divisible by 9?
- Q4.Divisibility test for 6 requires:
- Q5.Which is divisible by 11? (alternating sum)