Rules of Divisibility

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, , 68874

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

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) (08 can be divided by 4)

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) (last digit is a 0)

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) (last digit is even and =24 can be divided by 3)

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.

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]) (last three digits divisible by 8 [8x32=256])

Divisible by 9? If the sum of the digits is divisible by 9. All of these are divisible by 9: 6543 ( =18 which is divisible by 9) ( =27 which is divisible by 9)

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

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