What is the greatest number which when divides 92 and 215, leaves remainders 7 and 11, respectively?

Correct option is A

Given:

We need to find the greatest number which when divides 92 and 215, leaves remainders 7 and 11, respectively.

Solution:

Let the required number be d

For 92, the modified number will be 92 - 7 = 85

For 215, the modified number will be 215 - 11 = 204

First, we calculate the GCD of 85 and 204 using the Euclidean algorithm:

204 ÷ 85 = 2 remainder 34

85 ÷ 34 = 2 remainder 17

34 ÷ 17 = 2 remainder 00

Since the remainder is 0, the GCD of 85 and 204 is 17

Thus, the greatest number is 17