Factoring tests

There are ways to easily check to see if a large number is divisible by a smaller number.

1: All numbers are divisible by 1, even prime numbers.

2: Even numbers are divisible by 2. An even number is any number that ends in 0, 2, 4, 6, or 8.

3: When you sum the digits of your large number, if that sum is divisible by 3, then the original number is divisible by 3. Here is an example.

417

4+1+7 = 12
1+2 = 3

3 is divisible by 3 so 417 is divisible by 3.

5: If the number ends in 0 or 5 (excluding 0 itself) then the number is divisible by 5.

9: This is similar to 3. Sum the digits of the larger number, if they sum to a multiple of 9, then the original number is divisible by 9. Here is an example:

459
4+5+9 = 18
1+8 = 9

9 is divisible by 9 therefore 459 is divisible by 9.

10: If the number ends in 0 (excluding 0 itself) then the original number is divisible by 10.


Advanced hint:
When summing digits to check for 3 and 9 divisibility, you can skip adding in the 9's. One day I'll post why that is but until then, give it a try and see for yourself that you can just skip over the 9's.