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Rules of Divisibility

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Divisible by 2? If the last digit is even then the number is divisible by 2. Even digits are 0, 2, 4, 6 and 8 (yes zero is even!) All of these are divisible by 2: 546, 12, 154870, 68874

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Divisible by 3? If the sum of the digits is divisible by 3. All of these are divisible by 3: 3126 (3+1+2+6=12 which can be divided by 3) 87 (8+7=15 which can be divided by 3) 654831 (6+5+4+8+3+1=27 which can be divided by 3)

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Divisible by 4? If the last two digits are divisible by 4. All of these are divisible by 4: 916 (16 can be divided by 4) 9428 (28 can be divided by 4) 65498708 (08 can be divided by 4)

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Divisible by 5? If the last digit is 0 or 5. All of these are divisible by 5: 150 (last digit is a 0) 6545 (last digit is a 5) 6549840 (last digit is a 0)

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Divisible by 6? If the number is divisibly by both 2 and 3. All of these are divisible by 6: 216 (last digit is even and 2+1+6=9 which can be divided by 3) 65472 (last digit is even and 6+5+4+7+2=24 can be divided by 3)

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Divisible by 7? If you double the last digit and take it away from the rest of the number and the answer is 0 or divisible by 7.

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Divisible by 8? If the last 3 digits are divisible by 8. All of these are divisible by 8: 9880 (last three digits divisible by 8 [8x110=880]) 2123256 (last three digits divisible by 8 [8x32=256])

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Divisible by 9? If the sum of the digits is divisible by 9. All of these are divisible by 9: 6543 (6+5+4+3=18 which is divisible by 9) 3548124 (3+5+4+8+1+2+4=27 which is divisible by 9)

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Divisible by 10? If the last digit is a 0. All of these are divisible by 10: 320 122450 212549840

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Lots more… There are divisibility rules for larger numbers and there are other rules (tests) for the ones shown here.

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Divisibility Rules 01 Number Theory

Divisibility Rules 01 Number Theory

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