Question

If an integer ends in the digit 0 and the sum of its digits is divisible by $3$, then how many of the numbers 2, 3, 4, 5, 6, 8, 9 necessarily divide it

Answer 1

Given the equation, we can account for several notes:

• The integer ends in 0, meaning it’s divisible by 10

• It’s also divisible by 3

• It also must be divisible by 30 since 10 and 3 are factors of 30

If an integer ends in the digit 0 and the sum of its digits is divisible by 3, then only 3 and 6 would fit in the variable’s place, being divisible by 10 (as in 30 divided by 10 or 60 divided by 10) and 3 (as in 30 divided by 3 or 60 divided by 3).