If a ten-digit number 57a61395z2 is divisible by 72, then

Solution

ATQ,

Since, the number 57a61395z2 is divisible by 72, therefore it has to be divisible by 8 and 9, individually

If the number is divisible by 8, therefore last three digits should be divisible by 8

Hence, z = 0, 4 and 8

Now, check divisibility by 9

When z = 0, sum of the digits = 47 + a

Hence, a = 2

When z = 4, sum of the digits = 51 + a

Hence, a = 3

When z = 8, sum of the digits = 55 + a

Hence, a = 1

Therefore, number of possible values of a = 3