Which of the following is the greatest number that divides 72 and 119 and leaves 3 and 4 as respective remainders?

Explanation

Let the required number be denoted as d. Since d leaves a remainder of 3 when dividing 72, we can write: 72 - 3 = 69 Therefore, d divides 69 exactly. Similarly, since d leaves a remainder of 4 when dividing 119, we can write: 119 - 4 = 115 Therefore, d divides 115 exactly. Now, we need to find the greatest common divisor (GCD) of 69 and 115. Prime factorization of 69: 69 = 3 × 23 Prime factorization of 115: 115 = 5 × 23 The common factor is 23. Therefore, the greatest number that divides both 72 and 119, leaving remainders 3 and 4 respectively, is 23.