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

Answer:

13

Step-by-step 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 = HCF of 65, 117 [Since we need the largest number]

For this, 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.