Question

for what values of _ is 2,3_1 divisible by 9? by 3?

Answer 1

Any number is divisible by 9 if the sum of its digits divides by 9
so in 23X1, so far we have a sum of 6, so we need a 3
so 2331 is divisible by 9

the same rule applies for 3
Any number is divisible by 3 if the sum of its digits divides by 3
so in this case we could insert either a 0, 3, 6, or 9
that is, 2301, 2331, 2361, and 2391 are all divisible by 3