Question

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

Answer 1

Question:-

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

Answer:-

Thinking process :-

First , we subtract the remainders 5 and 8 from corresponding numbers respectively and then HCF of resulting numbers by using Euclid's division algorithm, which is the required largest number.

Solution:-

Since, 5 and 8 are remainders of 70  and 125 respectively.Thus, after subtracting these remainders from the numbers, we have the number 65 = (70 - 5), 117 = (125 - 8), which is divisible by the required number.

Now, required number = HCF of 65, 117               [for the largest number]

⇒ 117 = 65 × 1 + 52           [∵ dividend = divisor × quotient + remainder]

⇒ 65 = 52 × 1 + 13

⇒ 52 = 13 × 4 + 0

∴ HCF = 13

Hence, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8.

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.