Question

If the eight digit number 5668x25y is divisible by 48, find the least value of x+y

Answer 1

48 = 3 x 2⁴

=> Number should be divisible by 3, 2, 4, 8, 16

Using Divisibility rules of 2, y should be even.

=> y = (0,2,4,6,8)

Using divisibility rule of 4, 5y should be divisible by 4.

Only 52 & 56 divisible by 4.

=> y = (2,6)

Using divisibility rule of 8, 25y should be divisible by 8.

Only 256 divisible by 8.

=> y = 6

Using Divisibility rule of 3,

5 + 6 + 6 + 8 + x + 2 + 5 + 6 = 38 + x

=> x can be 1 or 4 or 7

Using divisibility rule for 16, x256 must be divisible by 16.

Only 4256 is divisible by 16.

=> x = 4

Required number = 56684256

x + y = 10