Question

Q5. What is the largest number
that divides 70 and 125, leaving
remainders 5 and 8
respectively?​

Answer 1

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.

Answer 2

Answer:

To find the largest no. That devides 70 and 125, with leaving remaind 5 and 8 respectively.

First step:

We will have to substract 5 and 8 from the given no.s

70-5= 65

125-8= 117

Second step:

Now, we will compute H.C.F (Highest common factor) of 65 and 117.

65= 1×5×13

117=1×3×3×13

Common factor = 1×13

H.C.F = 13

The required answer is 13

Is the largest number which devides 70 and 125 with leaving remainder 5 and 8.