51 --> 5+1 = 6, 6 is divisible by 3. This means that 51 is divisible by 3.

60 is divisible by 3, 60/3 = 20.

51 is 9 less than 60. 9 is divisible by 3. 9/3 = 3.

20 - 3 = 17.

Yep. If the sun of the numbers is divisible by 3, the number is divisible by three.

Works great for 6 too, as if it’s divisible by 3 and even, the number is divisible by 6.

And 9 is the same thing, but the sum has to be divisible by 9 (e.g. 12384 is divisible by 9 because the sum of the digits is 18, which is divisible by 9)

There’s also good rules for 4 and 8 as well. If the last 2 digits are divisible by 4, the whole number is (e.g. 127924 is divisible by 4 because 24 is) and if the last 3 numbers are divisible by 8, the whole number is (e.g. 12709832 is divisible by 8 because 832 is.)