Question

Take any three digit number. Reverse its digits and subtract the smaller of the two numbers from the larger. Determine what number always divides such differences for the following types of numbers.

Answer 1

Answer: 11 is the required number that always divides such differences for the following types of numbers.

Explanation:

Take any 3 - digit number, say, 325

On reversing its digit it becomes, 523

On subtracting the smaller of the two numbers from the larger,
`523-325\\\\=198`

we can see that 198 is an even number.

take another number say, 629

On reversing its digit, it becomes = 926

On subtracting , we get that

`926-629=297`

But 297 is not an even number.

But there is one common in both the cases is that both the differences are divisible by 11.

Hence, 11 is the required number that always divides such differences for the following types of numbers.