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

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answer is A.

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Detailed Solution

It is given that, a number which divides 70 and 125, leaving remainders of 5 and 8, respectively.
We have to find that number.
Subtract 5 from 70 and 8 from 125, and then we will find the largest number by the prime factorization method.

⇒ 70 − 5 = 65

and,

⇒ 125 − 8 = 117

Now, we will find the HCF of 65 and 117.
Prime factor of 65 and 117 are,

65 = 13 × 5

117 = 3 × 3 × 13

The product of each common prime factor's smallest power yields the HCF (highest common factor) of the numbers. Therefore, 13 is the HCF of 117.
Thus, 13 is the highest common factor of 70 and 125, leaving remainders of 5 and 8, respectively.
Hence, option 1 is correct.

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