Question

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is
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Answer 1

Answer:

70-5,125-8 are the numbers

65,117 are the numbers

The largest number which divides is means GCD of the number

gcd is 1 so,

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is 1

Answer 2

GIVEN:-

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

FIND:-

What is the number = ?

SOLUTION:-

Here,

when the number divides 70 leaves remainder as 5. So, 70-5 = 65

and

when the number divides 125 leaves remainder as 8. So, 125 - 8 = 117

Now, let us find the HCF of 65 and 117.

Since, 117>65

$\tt \therefore117 = 65 \times 1 + 52$

$\tt \implies65 = 52 \times 1 + 13$

$\tt \implies 52 = 13\times 4 + 0$

Hence, remainder is become 0.

Thus, 13 is the HCF of 65 and 117.

Hence, $\boxed{\tt13}$ is the required no. which divides 70 and 125 leaving remainder 5 and 8 respectively.