Question

3) Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively.

Answer 1

Answer:

13

Step-by-step explanation:

First we subtract 5 from 70 and 8 from 125 to make them completely divisible by that number

⇒ 70-5= 65

⇒ 125-8= 117

Now we find factors of these numbers

Factors of 65 = 1, 5, 13, 65

Factors of 117 = 1, 3, 9, 13, 39, 117

Common Factors = 1, 13

Highest Common factor (HCF) = 13  

∴ The required number = 13

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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.