Question

find the largest number which divides 70 & 125 , leave remainder 5 & 8 respectively.​
who will answer this question step by step , I will make that person brainliest.

Answer 1

Answer:

To find the largest number which divides 70 and 125 leaving the remainder 5 and 8 respectively, we will have to subtract 5 from 70 and 8 from 125 then we will compute the Highest Common Factor of those two number which we will get after subtracting.

a) 70 - 5 = 65

b) 125 - 8 = 117

Now, we will compute the H.C.F. of 65 and 117.

a) 65                                     b) 117

     _______                                  ________      

  5 |  65,                                     3 |  117

     |_______                                 |________

13 |  13                                      3 |   39

     |_______                                 |________  

     |    1                                    13 |   13

     |                                               |________

                                                     |     1

                                                     |

13 is the only common factor of 65 and 117. Hence H.C.F. of 65 and 117 is 13

Therefore, 13 is the largest number which divides 70 and 125 leaving the remainder of 5 and 8 respectively.

Let us check it.

a) 70 ÷ 13

Quotient = 5

Remainder = 5

b) 125 ÷ 13

Quotient = 9

Remainder = 8

Step-by-step explanation:

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.