Question

Find the largest number
which divides 70 and
125 leaving remainders
5 and 8 respectively...​

Answer 1

Step-by-step explanation:

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.

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Answer 2

Answer:

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

Step-by-step explanation:

For this , 117= 65 x 1 + 52 (ie. dividend = divisor x quotient + remainder)

= 65= 52 x 1 + 13

= 52= 13 x 4 + 0

ie

Hence, 13 is the largest number which divides 10 and 125, leaving remainders 5 and 8