Rules of Divisibility

The rules of divisibilty are rules which allow us to look at a number and straight away see if you can divide the number equally by others, leaving no remainder. The rules are as follows:

• If a number divides by 10 without a remainder then there will be a zero in the units column. So 340 will divide by 10 with no remainder, but 578 won't.

• If a number divides by 5 with no remainder then there will be either a 5 or a 0 in the units column. So 365 and 670 can be divided exactly by 5, but 408 can't.

• If a number divides exactly by 2 then it will have a 0, 2, 4, 6 or 8 in the units column (it will be even). So 364, 256, 48 can be divided exactly by 2, but 345, 567 and 649 can't.

• If a number divides exactly by 4 then its last 2 digits will be in the 4 times table. So 324 and 572 can divide exactly by 4 because 24 and 72 are in the 4 times table, whereas 234 and 458 can't, as 34 and 58 are not in the 4 times table.

• If a number divides by 8 then you take its last 3 digits, halve them and then see if the last 2 digits are in the 4 times table  e.g. 3456 is in the 8 times table because if you take the last 3 digis (456) and halve them you get 228, and 28 is in the 4 times table, so 3456 is in the 8 times table.

• If a number divides by 3, then the total of its digits will be a multiple of 3. So 456 can be divided by 3 because 4 + 5 + 6 = 15, and 15 is in the 3 times table i.e. a multiple of 3. 1003 cannot be divided by 3 because 1 + 0 + 0 + 3 = 4, and 4 is not a multiple of 3.

• If a number divides by 6 then firstly see if it is an even number, then see if it can be divided by 3. e.g. 276 can be divided by 6 because it is an even number and its digits add up to 15, so it can be divided by 3.

• If a number divides equally by 9 then the total of all its digits will be a multiple of 9. e.g. 8757 can be divided by 9 because 8 + 7 + 5 + 7 = 27, which is a multiple of 9.

Comments

[susan]

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Susan