Difference between the three digit number and the number formed by reversing its digit is always divisible by which number
Answers
Answered by
11
Let A, B, and C be the digits of the original number from left to right. Then the actual number is 100A + 10B + C. The number obtained by reversing this is 100C + 10B + A. The difference between the two is
| 100A+10B+C - (100C+10B+A) | =
| 99A - 99C | =
99 |A - C|
So the number is always divisible by 99.
Of course, this also means it's divisible by any factors of 99:
1, 3, 9, 11, 33, 99
Hope this will help u.... :-)
| 100A+10B+C - (100C+10B+A) | =
| 99A - 99C | =
99 |A - C|
So the number is always divisible by 99.
Of course, this also means it's divisible by any factors of 99:
1, 3, 9, 11, 33, 99
Hope this will help u.... :-)
Similar questions