Question

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

Answer 1

ur answer is 13

Explanation: Since 5 and 8 are the remainders of 70 and 125, respectively. Thus after subtracting these remainders from the numbers, we have the numbers

65 = (70 − 5), 117 = (125 − 8) which is divisible by the required number.

Now required number = H.C.F of (65,117)

117=65×1+52
65=52×1+13
52=13×4+0
H.C.F(65,117)=13

hope it's helps you

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.