Whole number - divisibility rules (video tutorial)

divisible by Rules Example
2 All even numbers are divisible by 2.
Ex., all numbers ending in 0,2,4,6 or 8.
1234 - Divisible by 2
1237 - Not divisible by 2
3 Add up all the digits in the number.
If the sum is divisible by 3 then the number is also divisible by 3.
Is 23457 divisible by 3?
1) 2 + 6 + 4 + 5 + 7 = 24;
2) 24: 2 + 4 = 6
3) 6 is divisible by 3; so 23457 is also divisible by 3
4 If the last 2 digits of a number is divisible by 4
then the number also divisible by 4
12320: Last 2 digits (20) is divisible by 4,
So 12320 is also divisible by 4.
5 If the last digit is a 5 or a 0, the number is divisible by 5. 4590: number ends with 0; 3265: number ends with 5
So both are divisible by 5.
6 If the number is divisible by 2 and 3 then it is divisible by 6 also.
Apply divisibility rule of 2 and 3.
2568 is divisible by 6 because it is divisible by 2 and 3.
1) Last digit (8) is even. So divisible by 2
2) sum of all digits: 2 + 5 + 6 + 8 = 21
3) 2 + 1 = 3 (3 is divisible by 3)
7 Double the last digit and subtract it from the rest of the number.
If the answer is divisible by 7 (or 0) then it is divisible by 7

This rule can be applied until the result is small enough to divide by 7.
Is 16184 divisible by 7?
1) 1618 - (2 * 4) = 1610
2) 161 - (2 *0) = 161
3) 16 - 2 = 14
4) 14 is divisible by 7. So 16184 is also divisible by 7.
8 If the last three digits of the number is divisible by 8 then the entire number is divisible by 8.
The following rule can be used for quick elimination.
Apply divisibility rule of 2 and 4, If it fails then the number can not be divided by 8.
Is 18512 is divisible by 8?
Last 3 digits of 18512 is 512. 512 is divisible by 8.
So 18512 is divisible by 8.
9 Add up all the digits in the number.
If the sum is divisible by 9 then the number is also divisible by 9.
11916 divisible by 9
1) 1 + 1 + 9 + 1 + 6 = 18
2) 1 + 8 = 9
3) 9 is divisible by 9.
10 If the last digit of the number is 0 then the number is divisible by 10. 23760: Last digit is 0 so it is divisible by 10.
34561: Last digit is not 0 so it is not divisible by 10.
11 Alternately add and subtract the digits from left to right. (Assume 0 is added to the first digit.)
If the result (including 0) is divisible by 11, the number is also.
365167484 is divisible by 11, start by subtracting: [0+]3-6+5-1+6-7+4-8+4 = 0;
therefore 365167484 is divisible by 11.
12 The number is divisible by both 3 and 4 then the number is divisible by 12.
Apply divisibility rule of 3 and 4.
2772 divisible by 12 because it is divisible by 3 and 4.
1) 2 + 7 + 7 + 2 = 18 ; 1 + 8 = 9. 9 is divisible by 3
2) last two digits of 2772 = 72. 72 is divisible by 4