The largest number which divides 70 and 125, leaving 5 and 8, respectively, isa) 13b) 65c) 875d) 1750

To find the largest number that divides 70 and 125, leaving remainders of 5 and 8, respectively, we need to use the concept of "congruence."

Let's consider the two given conditions:

When 70 is divided by the required number, the remainder is 5.
When 125 is divided by the same required number, the remainder is 8.
We can express these conditions as congruences:

70 ≡ 5 (mod n), where n is the required number.
125 ≡ 8 (mod n), where n is the required number.
Now, to find the required number, we need to find the common divisor of (70 - 5) and (125 - 8). That is:

70 - 5 = 65
125 - 8 = 117
The largest number that divides both 65 and 117 is the greatest common divisor (GCD) of 65 and 117.

Now, calculating the GCD of 65 and 117:
GCD(65, 117) = 13

So, the largest number that divides 70 and 125, leaving 5 and 8, respectively, is 13.

The correct option is: a) 13