Divisibility Rules
There are tricks to help you determine if a number is divisible by 2, 3, 4, 5, 6, 9, and 10. Use these quick tricks instead of dividing to find factors.
Rules and Examples
Easy, "Look-at-the-Number" Divisibility Rules
2- any even number (a number ending in 0, 2, 4, 6, 8) is divisible by 2
example - 746 is divisible by 2 because it ends in 6
4 - if the numbers in the tens and ones place is divisible by 4, then the whole number is divisible by 4.
example - 716......16 is divisible by 4, therefore 716 is divisible by 4.
5 - any number ending in 5 or 0 is divisible by 5
example - 630 is divisible by 5 because it ends in 0
example - 965 is divisible by 5 because it ends in 5
10 - any number ending in 0 is divisible by 10
example - 619,950 is divisible by 10 because it ends in 0
"Work-for-it" Divisibility Rules
These rules involve some work; you cannot just look at the number to determine divisibility.
3 - if the sum of the digits is divisible by 3, then the original number is divisible by 3
example - 252....2 + 5 +2 = 9 is divisible by 3, therefore, 252 is divisible by 3.
6 - if a number is divisible by BOTH 2 AND 3, then the number is divisible by 6.
example - 138 - 8 is even, so it is divisible by 2.....1 + 3 + 8 = 12 is divisible by 3. Since 138 is divisible by 2 and 3, then it is divisible by 6.
9 - if the sum of the digits is divisible by 9, then the original number is divisible by 9.
example - 963.....9 + 6 + 3 = 18 is divisible by 9, therefore 963 is divisible by 9.
Rules and Examples
Easy, "Look-at-the-Number" Divisibility Rules
2- any even number (a number ending in 0, 2, 4, 6, 8) is divisible by 2
example - 746 is divisible by 2 because it ends in 6
4 - if the numbers in the tens and ones place is divisible by 4, then the whole number is divisible by 4.
example - 716......16 is divisible by 4, therefore 716 is divisible by 4.
5 - any number ending in 5 or 0 is divisible by 5
example - 630 is divisible by 5 because it ends in 0
example - 965 is divisible by 5 because it ends in 5
10 - any number ending in 0 is divisible by 10
example - 619,950 is divisible by 10 because it ends in 0
"Work-for-it" Divisibility Rules
These rules involve some work; you cannot just look at the number to determine divisibility.
3 - if the sum of the digits is divisible by 3, then the original number is divisible by 3
example - 252....2 + 5 +2 = 9 is divisible by 3, therefore, 252 is divisible by 3.
6 - if a number is divisible by BOTH 2 AND 3, then the number is divisible by 6.
example - 138 - 8 is even, so it is divisible by 2.....1 + 3 + 8 = 12 is divisible by 3. Since 138 is divisible by 2 and 3, then it is divisible by 6.
9 - if the sum of the digits is divisible by 9, then the original number is divisible by 9.
example - 963.....9 + 6 + 3 = 18 is divisible by 9, therefore 963 is divisible by 9.
