Prove that: The difference between a three-digit number and the number formed by reversing the digits is always a - Maths - Integers

Question

Prove that:

​The difference between a three-digit number and the
number formed by reversing the digits is always a multiple of
99

Ankita Agarwal · Accepted Answer

Dear Student,

Suppose the three digit number is ABC, i
e
 100A+10B+C          
iNow, reversing the digit CBA i e
, 100C+10B+A                            
iiSubtracting ii from i100a+10B+c-100C+10B+A99A-99C99A-cTherefore the difference is always a multiple of 99
Hence Proved

Regards

Prove that: ​The difference between a three-digit number and the number formed by reversing the digits is always a multiple of 99

Prove that:

The difference between a three-digit number and the number formed by reversing the digits is always a multiple of 99