Deciding the divisibility made easier

Ever wondered how easy it is to find out whether a number is divisible by another number? Here are a few simple but powerful techniques which you can use to find out such secrets about numbers.

Divisible by 1

All numbers are divisible by 1

Divisible by itself

All numbers are divisible by itself

Divisible by 2

If a number is an even number, or in other words, if the last digit of a number is 0, 2, 4, 6 or 8, it is divisible by 2.

Divisible by 3

If you add the digits of a number repeatedly until you get a single digit, and if that single digit is 3, 6 or 9, the number is divisible by 3.

123 → 1 + 2 + 3 = 6 → divisible by 3

279 → 2 + 7 + 9 = 18 → 1 + 8 = 9 → divisible by 3

1478 → 1 + 4 + 7 + 8 = 20 → 2 + 0 = 2 → not divisible by 3

Divisible by 4

If the last 2 digits of a number are “00” or divisible by 4, then the number is divisible by 4

136 → the last 2 digits are divisible by 4, hence 136 is divisible by 4

1000 → the last 2 digits are “00”, hence 1000 is divisible by 4

206728 → the last 2 digits are divisible by 4, hence 206728 is divisible by 4

Divisible by 5

if the last digit of a number is either 5 or 0, that number is divisible by 5.

Divisible by 6

If the number is divisible by both 2 and 3, then the number is divisible by 6. Or in other words, if the number is even, and the sum of its digits yield a number divisible by 3, it is divisible by 6.

129 → is not an even number, hence not divisible by 6

1572 → is an even number, and 1 + 5 + 7 + 2 = 15 → 1 + 5 = 6, hence divisible by 6

Divisible by 7

Double the last digit and subtract it the remaining portion of the number. Do this repeatedly until you get a single digit. If the final single digit is 7 or 0, the number is divisible by 7.

714 → 71 – 8 → 63 → 6 – 6 = 0 hence 714 is divisible by 7

87654234 → 8765423 – 8 → 8765415 → 876541 – 10 → 876531 → 87653 – 2 → 87651 → 8765 – 2 → 8763 → 876 – 6 → 870 → 87 – 0 → 87 → 8 – 14 = -6, hence 87654234 is not divisible by 7

87654238 → 8765423 – 16 → 8765407 → 876540 – 14 → 876526 → 87652 – 12 → 87640 → 8764 – 0 → 8764 → 876 – 8 → 868 → 86 – 16 → 70 → 7 – 0 = 7, hence 87654238 is divisible by 7

Divisible by 8

If the last 3 digits of a number are “000” or divisible by 8, the number is divisible by 8.

25200 –> last 3 digits “200” is divisible by 8, hence 25200 is divisible by 8

Divisible by 9

if you add the digits of a number repeatedly until you get a single digit, and if that single digit is 9, the number is divisible by 9.

5670 –> 5 + 6 + 7 + 0 = 18 –> 1 + 8 = 9, hence 5670 is divisible by 9

Divisible by 10

If the last digit of a number is 0, it is divisible by 10.

Divisible by 11

Find out the sum of alternate digits, and then find the difference between the first sum and the second sum. If the difference is 11, the number is divisible by 11.

12345678 → (1+3+5+7) – (2+4+6+8) → 16 – 20 = -4, hence 12345678 is not divisible by 11.

123456839 → (1+3+5+8+9) – (2+4+6+3) = 26 – 15 = 11, hence 123456839 is divisible by 11.

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