Find all possible digits x, y, z such that the number 13xy45z is divisible by 792.

To be divisible by 792, a number must be divisible by 8 and 99. Then, the last 3 digits are divisible by 8. The only digit z such that 45z is divisible by 8 is 6. Therefore, z=6 and the number ends in 456. Since 13xy456 is divisible by 99, the sum of the digits in pairs is divisible by 99. Then, 1+3x+y4+56 is divisible by 99. The only possibility is 1+38+04+56=99. Therefore, x=8 and y=0. Then, the number is 1380456=792*1743.

Posted by Math Man on 2020-10-20 09:25:29