Question

When to numbers are individually divided by a particular divisor (greater than 1), they leave the same remainder. The difference between the numbers is 450. How many such divisors are possib
17
12​

Answer 1

Given : When 2 numbers are individually divided by a particular divisor (greater than 1), they leave the same remainder.  

The difference between the numbers is 450.

To Find : How many such divisors are possible

Solution:

Let say Numbers are  

A  ,  A + 450

A  =  bq   +  r

A + 450  = bk + r

=> 450 = b(k - q)

450 = 1 * 450

450 = 2 * 225

450 = 3 * 150

450 = 5 * 90

450 = 6 * 75

450 = 9 * 50

450 = 10 * 45

450 =  15 * 30

450 = 18 *  25

Total 18 -  but greater than 1  Hence  

18 - 1  = 17

17 Such Divisors are possible

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