So there's a trick to the divisibility rules:
2- if the last digit is even, it is divisible by 2.
3- add the digits together (ex. 123 - 1 + 2 + 3). The sum must be divisible by three for the number to be divisible by 3.
4- if the last 2 digits are divisible by 4, then the number is divisible by 4.
5- if the last digit is 0 or 5, the number is divisible by 5.
6- if the number is divisible by 2 AND 3, then it is divisible by 6.
9- like three, add the digits together (ex. 123 - 1 + 2 + 3). The sum must be divisible by nine for the number to be divisible by 9.
10. The ones digit is 0.
Knowing this knowledge, we can answer the problems.
1. 5 + 6 + 7 + 3 = 21
- 21 is divisible by 3 and 9. Therefore, 5,673 is divisible by 3 and 9.
2. 4,560-
- It ends in 0, so it is automatically divisible by 2 and 10.
4 + 5 + 6 + 0 = 15
- 15 is divisible by 3 but not 9.
Answer for #2: 4,560 is divisible by 2, 10, and 3.
3. 108,756
- It ends in 6, so it is automatically divisible by 2.
1 + 0 + 8 + 7 + 5 + 6 = 27
- 27 is divisible by 2 AND 9, so they are in too.
- It is also divisible by 6 because 108,756 is divisible by 2 and 3.
- It is not, however, divisible by 5 because it doesn't end in 0 or 5.
Answer to #3: 108,756 is divisible by 2, 3, 6, and 9.
