The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is (A) 13 (B) 65 (C) 875 (D) 1750

Correct answer is (A) 13

Solution:

Since, 5 and 8 are the remainders of 70 and 125, respectively.

Thus, after subtracting these remainders from the numbers, we have the numbers 65 = (70 – 5),

117 = (125−8), which is divisible by the required number.

Now, required number = HCF of 65, 117 [Since we need the largest number]

For this, 117 = 65×1+52 [∵ dividend = divisor × quotient + remainder]

⟹ 65 = 52×1+13

⟹ 52 = 13×4+0

∴ HCF = 13

Hence, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8.

Number when divides 70 and 125 leaves remainders 5 and 8, then

70−5=65

125−8=117

Then HCF of 65 and 117 is

65=5×13
117=3×3×13

Hence, HCF of 65 and 117 is 13.

13 is the largest number which divides 70 and 125 and leaves remainders 5 and 8.