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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.
Updated on: 10-Oct-2022
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