Determine the largest number that, when used to divide 1300, 4630, and 6850, leaves the same remainder in each case. Additionally, identify the common remainder.

To solve this problem, we need to find the greatest common divisor (GCD) of the differences between the numbers.

Step 1: Find the differences between the numbers.

• 4630 - 1300 = 3330
• 6850 - 4630 = 2220
• 6850 - 1300 = 5550

Step 2: Find the GCD of these differences. The GCD of 3330, 2220, and 5550 is 1110.

So, the largest number that can divide 1300, 4630, and 6850 leaving the same remainder is 1110.

Step 3: Find the common remainder. To find the common remainder, we can divide one of the original numbers by the GCD.

• 1300 ÷ 1110 = 1 remainder 190

So, the common remainder when 1300, 4630, and 6850 are divided by 1110 is 190.