Question

Test 43,785 for divisibility by 2, 3, 5, 9, and 10.

Answer 1

43785 is not divisible by 2 because it's not an even number, and this also means it's not divisible by 10 because 10 = 2*5.

The sum of its digits is 4 + 3 + 7 + 8 + 5 = 27, which is divisible by 3 since 27 = 3*9, so 43785 is divisible by 3. We have 43785 = 3*14595.

It would be divisible by 9 if 14595 were also divisible by 3. That number has digital sum 1 + 4 + 5 + 9 + 5 = 24, which is divisible by 3, so 14595 is too and 14595 = 3*4865. So 43785 = 9*4865, and it is indeed divisible by 9.

14595 is clearly divisible by 5 because its ends with a 5.