division

A three digit number is entered twice into the calculator. What will be the Remainder when the number in the calculator is divided by 91.




let the number be abc
so the number entered into calculator = abcabc
100000a + 10000b + 1000c +100a + 10b + c
= 100100a + 10010b + 1001c
= 1001 [ 100a + 10b + c]

now the prime factors of 1001 are 11, 7 and 13.
Therefore, when the number is divided by 91 (i.e. 7 x 13) the Remainder is zero