Divisibility Rules

By: Jack, Mirko, and Diego

Divisibility Rules for Even Numbers

To divide by 2 - The number must be even; the number in the ones place must be 0, 2, 4, 6, or 8

Ex: 348 can be divided by 2 because the last number is even.



To divide by 4 - The last 2 digits will form a number divisible by 4

Ex: 10,548 can be divided by 4 because the last 2 digits are divisible by 4.



To divide by 6 - If it is divisible by both 2 and 3

Ex: 816 can be divided by 6 because it is divisible by both 2 and 3. It is divisible by 2 because it is even. It is divisible by 3 because the sum of the digits (15), is divisible by 3.



To divide by 10 - The last digit must end in 0

Ex: 970 can be divided by 10 because the number ends in a 0.



Divisibility Rules for Odd Numbers

To divide by 3 - The sum of digits divides by three

Ex: 123,456 can be divided by 3 because the sum of all the digits is divisible by 3.



To divide by 5 - Ending in 5 or 0

Ex: 345 can be divided by 5 because 345 ends in a 5.



To divide by 9 - The sum of it's digits divides by 9

Ex: 873 can be divided by 9 because the sum of the digits is divisible by 9.


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Examples

345 is divisible by:

- 3 because the sum of all three digits is divisible by 3

- 5 because the number ends with a 5


345 is NOT divisible by: 2, 4, 6, 9, and 10 because it is not even, the last two digits are not divisible by 4, the digits are not divisible by both 2 and 3, the sum of the digits is not divisible by 9, and the last digit is not a 0.


642 is divisible by:

- 2 because it is even

- 3 because the sum of the digits is divisible by 3

- 6 because it is divisible by 2 and 3


642 is NOT divisible by: 4, 5, 9, and 10 because the last 2 digits are not divisible by 4, the number doesn't end in a 5 or 0, the sum of the digits is not divisible by 9, and the number doesn't end in a 0.


444 is divisible by:

- 2 because it is even

- 3 because the sum of the digits is divisible by 3

- 4 because the last 2 digits are divisible by 4

- 6 because it is divisible by 2 and 3


444 is NOT divisible by: 5, 9, and 10 because the number doesn't end in a 5 or 0, the sum of the digits is not divisible by 9, and the number doesn't end in a 0.