_72_ what numbers do i need to put in underlines to get 4-digit number divisible by 45. Find largest such number

Answer 1

A number divisible by 45 will also have to be divisible by 5 and by 9. A number divisible by 5 has to end in 0 or 5. So that gives us two cases: 1) The number looks like _720 2) The number looks like _725

In order for a number to be divisible by 9, the sum of its digits must also be divisible by 9.

So in case 1) _720, the sum of the known digits 7 + 2 + 0 = 9. So the missing digit must either be 9 (or 0 but that would give us a 3-digit number). So that gives us 9720.= 216*45

In case 2) _725, the sum of the known digits 7+2+5 = 14. And the only digit which will give us a multiple of 9 when added is 4. And that gives us 4725 = 105*45

The larger of the two is 9720