Divisibility Rules: From 2-10
Divisibility of 2
This is one divisibility rule that most people are probably familiar with. If the last digit in a number is even, the number is divisible by 2. For example, 44444 is divisible by 2, but 44445 is not.
Divisibilities of 3 and 9
To find out whether a number is divisible by 3 or 9, add up the digits in the number. If the result is divisible by 3, then the original number was too. If the result is divisible by 9, then so was the original number. For example, take the number 44445. 4+4+4+4+5 = 21. The number 21 is divisible by 3, but not divisible by 9. Therefore, the number 44445 is also divisible by 3, but not by 9.
Divisibilities of 4 and 8
To check whether a number is divisible by 4, see whether the last two digits are divisible by 4. To check whether a number is divisible by 8, see whether the last three digits are divisible by 8. For example, take the number 44444. The last two digits are 44, and 44 is divisible by 4. But the last three digits are 444, which is not divisible by 8. Therefore, the number 44444 is divisible by 4, but not by 8.
Divisibilities of 5 and 10
These are probably the second most commonly known rules – and definitely the easiest ones too! A number is divisible by 10 if the last digit in the number is 0. It is divisible by 5 if the last digit in the number is either 5 or 0. For example, 44445 would be divisible by 5 because its last digit is a 5. However, it would not be divisible by 10 because its last digit is not a 0.
Divisibility of 6
To find out if a number is divisible by 6, check to see if it is divisible by both 2 and 3 (because 2X3=6). For example, the number 44444 is divisible by 2, but not by 3, so it is not divisible by 6.
Divisibility of 7
The rule to help you figure out if a number is divisible by 7 is a little complicated. First, take the last digit of a number. So if the number was 161 you would take 1. Double the number (1 x 2 = 2), and then subtract that number from the remaining digits: 16 - 2 = 14.
14 is obviously divisble by 7, so that means the entire number is divisible by 7.
If it is a large number you can repeat the process until the number is down to a manageable level. Example:
Start with 5278
Double 8. You end up with 16.
Subtract from 527. You end up with 511.
Double 1. You end up with 2.
Substract from 51. You end up with 49, which is divisible by 7. Now you know the whole number is divisible by 7.
Now here’s the original problem again: Which one-digit numbers go into 78,000? Easier now, isn’t it? Since the last digit is a 0, the numbers 2 and 5 both go into it. It’s divisible by 4 and 8 because any number goes into 000 or 00. Adding up the digits gives you 15, which is divisible by 3, but not by 9. Since it’s divisible by both 2 and 3, it’s also divisible by 6. And as for 7…I’ll leave that one to you.