Question

what is the greatest integer that leaves the same remainder when divided into each of the intgers 3712, 3814, and 3865

Answer 1

51

Step-by-step explanation:

To find the greatest integer that leaves the same remainder when divided into each of the integers 3712, 3814, and 3865, we can find the greatest common divisor (GCD) of the differences between these integers.

First, calculate the differences:

3814 - 3712 = 102

3865 - 3814 = 51

Now, calculate the GCD of these differences:

GCD(102, 51) = 51

Therefore, the greatest integer that leaves the same remainder when divided into each of the integers 3712, 3814, and 3865 is 51.