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Q.

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


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Detailed Solution

Concept- That number would be 13. Finding the number with the highest common factor after subtracting the remainder from the provided numbers yields the largest number. That provides us with the highest total. Because it was indicated before that the number divides the supplied number and leaves a residual, we must subtract the remainder in order to obtain the number that can be divided by the biggest number.
Let's start with the number 70. It was stated that when 70 is divided by the largest number, 5 is left behind.
The leftover is 8 when the number 125 is divided by the largest number.
Consider 70 once more.
The largest number divides 70 and leaves 5 as the remainder, thus we must deduct 5 from 70.
70-5=65.
Now, when we write the factors for 65, we obtain 65=13×5.
The largest number divides 125 and leaves 8 as the remainder, thus we must deduct 8 from 125.
125-8=117.
Now that we have written the factors for 117, we have 117=3×3×13.
We must determine H.C.F., the largest number that divides the two numbers (Highest common factor) .
65=13×5 
117=3×3×13.
G.C.F of 70 and 125 is 13
Hence, the correct option is 13.
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