Question

Find all digits x, y such that is divisible by 36.

Answer 1

To be divisible by 36 = 4 ´ 9, the number 34x5y should be divisible by 4 and 9.

Now, sum of the digits = 3 + 4 + x + 5 + y = 12 + x + y

The number 34x5y will be divisible by 9, if x + y = 6 or 15

Thus, the possible values of x and y are x = 0, y = 6 or x = 6, y = 0 or x = 2, y = 4 or x = 4, y = 2 or x = 6, y = 9 or x = 9, y = 6

So, the possible numbers are 34056, 34650, 34254, 34452, 34659 and 34956

Among these, 34056, 34452 and 34956 are divisible by 4.

Hence, x = 0, y = 6 or x = 4, y = 2 and x = 9, y = 6