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

**(A)** 13

**(B)** 65

**(C)** 875

**(D)** 1750

Given:

70 and 125

To find:

Here we have to find the value of the greatest number which divides 70 and 125 leaving remainders 5 and 8 respectively.

Solution:

If the required number divide 70 and 125 leaving remainders 5 and 8 respectively, then this means that number will divide 65($=70-5$) and 117($=125 - 8$) completely.

Now, we just have to find the HCF of 65 and 117.

__Finding HCF of 65 and 117 using Euclid's division lemma__:

Using Euclid’s lemma to get:

- $117\ =\ 65\ \times\ 1\ +\ 52$
- $65=52\times1+13$
- $52=13\times4+0$

Therefore the HCF of 65 and 117 is the divisor at this stage, i.e., **13**.

So, the greatest number which divides 70 and 125 leaving remainders 5 and 8 respectively is 13.

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