What is the greatest number that when divides 718, 1085 and 1179 leaves remainders 5, 4 and 6, respectively?

Correct option is D

Given:

When the greatest number divides 718, the remainder is 5.
When the greatest number divides 1085, the remainder is 4.
When the greatest number divides 1179, the remainder is 6.

Concept Used:

If a number x divides a number y leaving a remainder r, then (y - r) is divisible by x.
We will find the GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of the numbers (718-5), (1085-4), and (1179-6).

Solution:

Subtract the remainders from each number:
718 - 5 = 713
1085 - 4 = 1081
1179 - 6 = 1173
 Prime Factorization of the numbers:
- 713 = 23 × 31
- 1081 = 23 × 47
- 1173 = 3 × 7 × 7
 Identify the common factors:
- The only common prime factor is 23.
- Therefore, the GCD or HCF of 713, 1081, and 1173 is 23.
Thus, the greatest number that divides 718, 1085, and 1179 and leaves remainders 5, 4, and 6, respectively, is 23.