If 9A4156B is divisible by 88, then what is the minimum value of A * B?Options :0125

The given number is 9A4156B.

A number is divisible by 88 if it is divisible by both 8 and 11 (since 88 is a product of 8 and 11).

1. For a number to be divisible by 8, the last three digits must be divisible by 8. So, we have 56B. The possible values of B that make 56B divisible by 8 are 0, 4, and 8.

2. For a number to be divisible by 11, the difference between the sum of the digits at odd places and the sum of the digits at even places must be either 0 or a multiple of 11. So, we have (9+A+1+6) - (4+5+B) = 7+A-B.

If B=0, then A=4 to satisfy the divisibility rule of 11. If B=4, then A=7 to satisfy the divisibility rule of 11. If B=8, then A=0 or 11 to satisfy the divisibility rule of 11.

The minimum value of A*B is when A=0 and B=8, which is 0.

So, the minimum value of A*B is 0.