Question

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

Answer 1

It is given that on dividing 70 by the required number, there is a remainder of 5. This means that 70 − 5 = 65 is exactly divisible by the required number.
Similarly, 125 − 8 = 117 is exactly divisible by the required number.
The required number is HCF of 65 and 117.
By Euclid's division algorithm,
$$\begin{gathered} 117=65\times 1+52 \\ \Rightarrow 65=52\times 1+13 \\ \Rightarrow 52=13\times 4+0 \end{gathered}$$
Here, the remainder is zero. Therefore, the HCF of 65 and 117 is 13.
So, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8, respectively.

Hence, the correct answer is option A.