Question

find the largest number which divides 70 and 125 leaving remainders 5 qnd 8 respectively

Answer 1

Hi ,
__________________________
The largest number by which x , y

divisible and gives the remainder a ,

and b is

the HCF of ( x - a ) and ( y - b)
__________________________

According to the given problem ,

The largest number which divides

70 and 125 leaving remainders 5 and

8 respectively are

HCF of ( 70 - 5 ) = 65 and

( 125 - 8 ) = 117

65 = 5 × 13

117 = 3 × 3 × 13

HCF ( 65 , 117 ) = 13

Required number is 13.

I hope this helps you.

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Answer 2

Answer:-

Thinking process :-

First , we subtract the remainders 5 and 8 from corresponding numbers respectively and then HCF of resulting numbers by using Euclid's division algorithm, which is the required largest number.

Solution:-

Since, 5 and 8 are remainders of 70  and 125 respectively.Thus, after subtracting these remainders from the numbers, we have the number 65 = (70 - 5), 117 = (125 - 8), which is divisible by the required number.

Now, required number = HCF of 65, 117               [for the largest number]

⇒ 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.