Find the largest number that divides 70 and 125 and leaves remainders as 5 and 8 respectively.

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answer is B.

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Detailed Solution

Given are the numbers 70 and 125.
We have to find the largest possible number which divides 70 and 125 and leaves the remainders 5 and 8 respectively.
This implies that for 438 and 606 to be exactly divisible by the largest number, the given remainders must be zero.
So, we will subtract the remainder 5 from 70 and the remainder 8 from 125.
70 – 5 = 65
125 – 8 = 117
Now, this largest number will be the HCF of 65 and 117.
So, we proceed with the prime factorization of 65 and 117, to get their HCF as follows,

65 = 13 × 5 117 = 13 × 3 × 3

So, the common factor among the two numbers is 13.
Therefore, HCF (65, 117) = 13.
So, the largest number which divides 70 and 125 leaving the remainders 5 and 8 respectively is 13.
Hence, the correct option is 2.

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