basic math question

[Didymus]

I'm introducing my daughter to math and I can't remember if there's a quick rule to check if a large number is divisable by 7 and 8 at a glance.

 

1: if it's whole

2: if it's even.

3: if the digits add up to 3,6 or 9

4: if the 10s digit is even and the 1s digit is 0,4,8 or the 10s digit is odd and 1s digit is2,6

5: if it ends in 0,5.

6: if 2 and 3 both work.

7: ?

8: ? Can't think of a simple rule

9: digits add to 9

10: ends in 0

0: everything is divisable by 0. Haters gonna hate.

 

 

... I think when I was in school they said there wasn't one for those... But they said the same thing about 4.

Edited November 28, 2013 by Didymus

[John]

Divisibility by 7 can be checked by doubling the last digit, subtracting that from the number formed by the rest of the digits, and seeing if the result is divisible by 7. For example, given 315, you'd double 5 to get 10, then take 31-10 to arrive at 21, which is divisible by 7. Thus, 315 is divisible by 7. The method can be applied recursively.

A number is divisible by 8 if its last three digits are divisible by 8. I guess to check the last three digits, see whether it's even. If so, divide by 2, then see if the resulting number is divisible by 4.

Edited November 28, 2013 by John

[Didymus]

Thanks