Divisibility by 7 Tips

  • Double and Subtract Method: Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, then the original number is too.
  • Example: For 343 → 34 - (2×3) = 34 - 6 = 28, which is divisible by 7.
  • Block Method: Group digits in blocks of 3 from right to left, then alternately add and subtract these blocks. If the result is divisible by 7, so is the original number.

Divisibility by 8 Tips

  • Last Three Digits: A number is divisible by 8 if its last three digits form a number divisible by 8.
  • Example: 12,416 is divisible by 8 because 416 ÷ 8 = 52.
  • Even Hundreds: If the hundreds digit is even, check if the last two digits are divisible by 8. If the hundreds digit is odd, check if the last two digits + 4 are divisible by 8.

Divisibility Rules

Divisible by 2

The last digit is even (0, 2, 4, 6, or 8).

Example: 128 is divisible by 2 because it ends with 8.

Divisible by 3

The sum of all digits is divisible by 3.

Example: 381 (3+8+1=12) is divisible by 3.

Divisible by 4

The last two digits form a number divisible by 4.

Example: 7,316 is divisible by 4 because 16 is divisible by 4.

Divisible by 5

The last digit is 0 or 5.

Example: 295 is divisible by 5 because it ends with 5.

Divisible by 6

The number is divisible by both 2 and 3.

Example: 114 is even and 1+1+4=6 is divisible by 3.

Divisible by 7

Double the last digit and subtract it from the rest of the number. Repeat if needed.

Example: 343 → 34 - (2×3) = 28, which is divisible by 7.

Divisible by 8

The last three digits form a number divisible by 8.

Example: 12,416 is divisible by 8 because 416 ÷ 8 = 52.

Divisible by 9

The sum of all digits is divisible by 9.

Example: 2,187 (2+1+8+7=18) is divisible by 9.

Divisible by 10

The last digit is 0.

Example: 9,370 is divisible by 10 because it ends with 0.

Divisible by 11

The alternating sum of digits is divisible by 11.

Example: 1,364 → (1-3+6-4)=0, which is divisible by 11.