## Divisibility Rules

### Divisibility: Learn

Sometimes we need to know if one number will divide into another without
a remainder. We call this idea *divisibility*, and one number is
*divisible* by another if the division produces no remainder.

For example, divisibility might answer a question like, "Is the number 216 divisible by 3?" And the answer, is yes, the number 216 is divisible by 3 because 216 ÷ 3 = 72 with no remainder.

To find out if one number is divisible by another, you may have to use long division or a calculator. However, some numbers have easy rules to follow to determine divisibility quickly.

2: A number is divisible by 2 if it is even.

Example: 14 is divisible by 2 because it is even.

3: A number is divisible by 3 if its digits are divisible by 3.

Example: 216 is divisible by three because 2+1+6=9 and 9 is divisible by 3

4: There are two easy ways to tell if a number is divisible by 4. First, you could look at the last 2 digits--if they are divisible by 4 then the whole number is. Or, you could try to divide the number by 2 twice. If you get whole result, then it is divisible by 4. (This is because 2*2=4)

Example: 80 is divisible by 4 because 80/2 = 40 and 40/2 = 20, a whole number result

6: Check divisibility for 2 and 3. Any number that is divisible by both 2 and 3 is also divisible by 6. This is because 2*3=6.

7: There is no easy divisibility rule for seven. If you are trying to determine divisibility by 7 quickly, you may want to use a calculator. Otherwise try long division.

8: Much like with 4, there are two good options. First, if the last 3 digits are divisible by 8 then the whole number is. Or, you could try to divide the numer by 2 three times. If you get a whole result, then it is divisible by 8. (This is because 2*2*2=8)

Example: 216 is divisible by 8 because 216/2 = 108 and 108/2 = 54 and 54/2 = 27, a whole number result

9: A number is divisible by 9 if its digits are divisible by 9.

Example: 216 is divisible by nine because 2+1+6=9 and 9 is divisible by 9

10: Any number ending in zero is divisible by 10.

Larger numbers: The divisibility rules get a little tougher as the numbers get larger. Look for composite rules, like for 6, where if two smaller numbers are divisors, then their product is also a divisor.

### Divisibility: Practice

#### Is it divisible?

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Is the number divisible by the number ?

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