What is the smallest digit that can be placed in the blank so that 8-6935 can be divisible by 3?

Answer 1

2.

To test a number to be divisible by 3, add up the digits and if the sum is divisible by 3, so is the original number. If not, the excess over a multiple of 3 gives the remainder when the original number is divided by 3.

Subtract this remainder from 3 and this gives the smallest digit to replace the blank; unless the remainder is 0, in which case the blank can be replaced by a 0:

8 + 6 + 9 + 3 + 5 = 31 → 31 ÷ 3 = 10 remainder 1

Replace blank by 3 - 1 = 2:

826935 is divisible by 3

Answer 2

3