Question

find the greatest number that will divide 57, 93 and 191 so as to leave the same remainder in each case.

Answer 1

The greatest number that will divide 57, 93, and 191 to leave the same remainder is the greatest common divisor of the differences between the numbers, which is 2.

Step-by-step explanation:

To find the greatest number that will divide 57, 93, and 191 so as to leave the same remainder in each case, we need to calculate the differences between the numbers and then find the greatest common divisor (GCD) of those differences. Let's calculate the differences:

• 93 - 57 = 36
• 191 - 93 = 98
• 191 - 57 = 134

We can see that 36 is a common factor. However, for the GCD, we need to ensure it divides into all differences. To find the GCD of 98 and 134, we use the Euclidean algorithm:

1. Divide 134 by 98, remainder is 36.
2. Divide 98 by 36, remainder is 26.
3. Divide 36 by 26, remainder is 10.
4. Divide 26 by 10, remainder is 6.
5. Divide 10 by 6, remainder is 4.
6. Divide 6 by 4, remainder is 2.
7. Divide 4 by 2, remainder is 0. So, 2 is the GCD.

Therefore, the greatest number that divides 57, 93, and 191 leaving the same remainder is 2.