Question 51

x is the greatest number by which, when 2460, 2633 and 2806 are divided, the remainder in each case is the same. What is the sum of digits of x?

Solution

As given in the question, the remainder is the same in each. So (2633-2460), (2806-2460) and (2806-2633) should be completely divisible by 'x'.

(2633-2460) = 173

(2806-2460) = 346

(2806-2633) = 173

As we know that 173 is a prime number. So the HCF of (173, 346 and 173) will be 173.

Hence x = 173

Sum of digits of x = 1+7+3

= 11

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