Question

The largest number which divides 70and 125, leaving remaindets5 and 8 respectively?? ​

Answer 1

Step-by-step explanation:

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

LET '$x$' BE THE NUMBER.

$70\div x=Q_1...5$

$125\div x=Q_2...8$

$xQ_1+5=70$ and $xQ_2+8=125$.

Thus, $xQ_1=65$ and $xQ_2=117$.

Then $x$ should be the G.C.D of 65 and 117.

(As $x$ divides both number without any remainder.)

(Why G.C.D? Because we need the largest $x$.)

There is the answer, $x=13$.

ANS : 13