Divisibility Rules for 7 and 8

Hello friends! We've talked about divisibility rules for 2, 3, 4, 5, 6, 9, and 10; let's talk about 7 and 8, which may seem a little more complicated, but are easy to deal with once you get used to them. :)

In order to see if a number is divisible by 8, you only must check to see whether the last three digits of the number are divisible by 8. If they are, then the entire number is divisible by 8 too. 

Example 1: Is the number 8347475537272 divisible by 8? 
Answer 1: Yes, because the last 3 digits, 272, are divisible by 8.

Example 2: Is the number 314159265358979323846divisible by 8?
Answer 2: No, because the last 3 digits, 846, are not divisible by 8.

In order to see if a number is divisible by 7, you must/;

1. Take the last digit of the number you’re testing and double it. 
2. Then, subtract this number from the rest of the remaining digits. 

*If this new number is either 0 or a number that’s divisible by 7, then then original number is divisible by seven. 

Example 1: Is the number 364 divisible by 7? 
Answer 1: Yes: Double the 4 to get 8. Subtract 8 from 36 to get 28. Since 28 is divisible by 7, we can now say for certain that 364 is also divisible by 7.

Example 2: Is the number 8256 divisible by 7? 
Answer 2: No, Double 6 to get 12. Subtract 12 from 825 to get 813. 813 is slightly too large to tell whether it is divisible by 7 so we must repeat the process. Double 3 to get 6. Subtract 6 from 81 to get 75. Since 75 is not divisible by 7, neither is 813 or 8256. Therefore, 8256 is not divisible by 7.