Find the greatest integer that divides 358, 376, and 334 and leaves the same…

Step-by-Step Solution

To find the greatest integer that divides three numbers (A, B, and C) and leaves the same remainder in each case, follow these steps:

1. Calculate the pairwise differences: When a divisor leaves the same remainder for multiple numbers, it must also divide the differences between those numbers evenly.

   • Difference 1: |376 - 358| = 18

   • Difference 2: |376 - 334| = 42

   • Difference 3: |358 - 334| = 24

2. Find the HCF of the differences: The greatest integer we are looking for is the Highest Common Factor (HCF) of 18, 42, and 24.

   • Prime factorization of 18: 2 * 3 * 3

   • Prime factorization of 42: 2 * 3 * 7

   • Prime factorization of 24: 2 * 2 * 2 * 3

3. Identify the common factors: The common prime factors are 2 and 3.

   • HCF = 2 * 3 = 6.