The largest number which divides 70 and 125, leaving remainders 5 and 8,respectively, is

To find the largest number that divides 70 and 125, leaving remainders of 5 and 8 respectively, we can use the concept of the greatest common divisor (GCD).

Step 1: Calculate the GCD of 70 and 125. To do this, we can use the Euclidean algorithm. We divide the larger number (125) by the smaller number (70) and find the remainder. Then, we divide the previous divisor (70) by this remainder. We continue this process until we reach a remainder of 0.

125 ÷ 70 = 1 remainder 55 70 ÷ 55 = 1 remainder 15 55 ÷ 15 = 3 remainder 10 15 ÷ 10 = 1 remainder 5 10 ÷ 5 = 2 remainder 0

Step 2: The GCD is the last non-zero remainder, which is 5.

Therefore, the largest number that divides 70 and 125, leaving remainders of 5 and 8 respectively, is 5.