Question

Let N be the greatest number which divides 1667 and 2045 and leaves a remainder of 16 and 13 respectively. The sum of the digits of N is

(A) 10

(B) 1

(C) 20

(D) 3

(E) 5​

Answer 1

Answer:

The final answer is A) 10

Step-by-step explanation:

Given,

We need to find the greatest number which on dividing with 1667 gives us a remainder of 16 and on dividing with 2045 gives us a remainder of 13. First we need to find the HCF of 1667 - 16 = 1651  and 2045 - 10 = 2032.

1651 = 13 * 127

2032 = 2 * 2 * 2 * 2 * 127

Hence the HCF of both these numbers is 127.

The sum of the digits of these numbers is  1 + 2 + 7 = 10

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