Question

the largest number which divides 70 and 125,leaving remainder 5 and 8 respectively is​

Answer 1

✵Question:

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

✵Answer:

The number leaves 5 as remainder on dividing 70.

☛The number completely divides 70-5 = 65

Also,

The number leaves 8 as remainder on dividing 125

☛The number completely divides 125-8= 117

↬So, we have to find the greatest number that completely divides 65 and 117,

⦾ We have to find the HCF of 65 and 117,

⇢65= 5× 13

⇢117= 3×3×13

$\large{ \therefore{ \boxed{ \green{ \bold{hcf \: of \: 65 \: and \: 117 \: = \: 13}}}}}$

☛Hence, The largest number that can be divided by 70 and 125 leaving remainder 5 and 8 is 13.

✵So final answer:

$\huge{ \boxed{ \bold{ \red{ = 13}}}}$

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.