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Math K-Plus

Arithmetic - Divisibility Rules Also Known As Rules Of Divisibility Make Division Much Easier To Learn

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Arithmetic Division Made Easy By Divisibility Rules


Division of numbers, particularly large ones, can be very difficult without paper and pencil or calculator. There are tricks to simplify dividing numbers - even large ones. We call these tricks Divisibility Rules or Rules Of Divisibility.


Division Made Easy

Number Is Divisible By


If The Number Meets This Condition


Example


2 If its last digit is 0, 2, 4, 6, or 8. Examples: 12345678 is divisible by 2 because the last digit is 8.

12345678 ÷ 2 = 6172839.

3 If the sum of its digits are divisible by 3. Example: 125172 is divisible by 3 because the sum of the digits is divided by 3.

1 + 2 + 5 + 1 + 7 + 2 = 18.
18 ÷ 3 = 6.

4 If its last two digits (taken together as a two-digit number) are divisible by 4. Example: 1520 is divisible by 4 because the last two digit number pair (20) can be divided by 4.

1520 ÷ 4 = 380.

5 If the number ends in 0 or 5. Example: 875 is divisible by 5 because the last digit ends in 5.

875 ÷ 5 = 175.

6 It's even and the sum of its digits are divisible by 3. Example: 1232718 is even because the last digit ends in 0, 2, 4, 6, or 8 - 8 in this case.

Let's do check two; sum the digits and make sure they can be divided by 3.

1 + 2 + 3 + 2 + 7 + 1 + 8 is 24 and 24 ÷ 3 = 8.

7 This rule applies to three digit numbers only: the quantity "2 x (hundreds digit) x ten's digit + (last digit)" is divisible by 7.
Example: 710 is divisible by 7.

((2 × 7) × (1)) + 0 = (14 × 1) + 0 = 14.

14 ÷ 7 = 2.

8 If the last three digits (taken together as a three-digit number) are divisible by 8. Example: 231912 is divisible by 8.

The last three digits are divisible 912 ÷ 8 = 114.

If this is true, then 231912 ÷ 8 = 28989 must be true.

9 The sum of its digits is divisible by 9.
Example: 18726354 is divisible by 9 because the sum of the digits is divisible by 9.

1 + 8 + 7 + 2 + 6 + 3 + 5 + 4 = 36.

36 ÷ 9 = 4.

10 If the number ends in 0. Example: 1234567890 is divisible by 10 because the end digit is 0.

1234567890 ÷ 10 = 123456789.