Question

What is a five digit number divisible by 4 and 9?

Answer 1

A number divisible by 9 is also by 3. And a number divisible by 4 is also by 2.

So, a number divisible by 4 and 9 with 5 digits?

We can think in multiples of 4*9 = 36.

But it’s easier looking at the two easy rules:

Multiples of 4: end in 00, 04, 08, 12, 16, 20….Multiples of 9: the sum of all digits is also a multiple of 9.

What do we have?

We can take all 5 digits and write 12312. Or 33354. Or 55764.

If you only need one number, to make it faster, work with 3+2, assuring the the first 3 are a multiple of 9, and the last two are a multiple of 4 that sums 9: 90000, 99000, 99900, 99936, 99972, 66600, 66636…

Answer 2

If the number is divisible by 4 and by 9, so is it divisible by 36. Thus I started with the multiplication 200*36=7200, then 1800=50*36 and took 36 away to arrive at the solution, the number 9972.