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

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                                     [for the largest number]

For this, 117 = 65 × 1 + 52 [∵ dividend = divisior × 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 amnd 8.

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