Question

Find the largest two-digit number which leaves the same remainder on dividing 2614 and 2458.
pl help me answer will be marked brainliest thanks guys

Answer 1

Given:

Two numbers 2614 and 2458 are divided by a two digit number  and leaves the same remainder.

To Find:

Find the largest 2 digit number which leaves same remainder on dividing 2614 and 2458.

Solution:

A number N when divided by a number n , it can be factorized as following:

  $N = nq + r$    ;

Where N is the number, n is the divisor , q is quotient and r is the remainder.

1)$2614 = n()q_{1} +r$

2)$2458= n(q_{2}) + r$

substract equation 1 from 2   ;

$2614-2458 = n(q_{1}-q_{2} )$    ;  

$156= n(q_{1} -q_{2})$    ;

$156 = (2)(2)(3)(13)$

We need to find the largest two digit number which satisfies the above equation

possible values of n = 13,2,3,6,39,78,52,156

out of these highest two digit number is 72

The largest two digit number which leaves same remainder on dividing 2614 and 2458 is 72