What are the divisibility rules for 6 7 8 9 10?

Answer 1

If a number is divisible by six, then it must also be divisible by both two and three. To check it then, you simply apply both rules for each of those:

Is it an even number?

Is the sum of it's digits divisible by three?

If both answers are yes, then the number is divisible by six.

To find out if a number is divisible by seven take it's last digit, double it, and subtract it from the remaining digits. If the result is divisible by seven, then the original number is as well.

For example is three 343 divisible by 7? Let's find out:

3 * 2 = 6, and 34 - 6 = 28. Is 28 divisible by seven? Yes, but if you're not sure, you can repeat the process. 8 * 2 = 16, 2 - 16 = -14. 14 is of course divisible by 7.

If the last three digits of a number are divisible by 8, then the entire number is. For example, I know that 10923485710234985723908471859256 is divisible by eight, because I know that the last three digits, 256, form a number that's divisible by eight. Not sure about those last three digits? Simply divide them by two, three times in a row. If the result is a whole number, then it's divisible by eight. 256 / 2 = 128, 128 / 2 = 64, 64 / 2 = 32, so 256 is divisible by eight, and therefore 10923485710234985723908471859256 is also.

If the sum of the digits is divisible by 9, then the number itself is. For example, is 8936523 divisible by 9? Well, 8 + 9 + 3 + 6 + 5 + 2 + 3 = 36. Is 36 divisible by 9? 3 + 6 = 9. 9 is obviously divisible by 9, so yes, 8936523 is also.

If the last digit is a zero, then the number is divisible by 10. For example, 12340 is divisible by ten, but 12345 is not.