Question

.The largest number which divides 60 and 125, leaving remainders 5 and 8 respectively is

Answer 1

Answer:

lcm→70,125 = 5*2*7, 5*5*5 = 5*2*7*5*5 = 1750

Series for 70 →5, 75, 145, 215,285………………………,5+70m

Series for 125→8,133,258,383,508,……………………….,8+125n

5+70m ←→ 8+125n

70m ←→ 3+125n

But if m & n are both integers then it’s impossible as 3+125n will always end with either 3 or 8 while 70m will end with 0 at the end.

Hence, There’s no integer which if divided by 70 & 125 leaves remainders of 5 & 8.

Answer 2

Answer:

1

Step-by-step explanation:

Solution :-

To find the largest number which divides 60 and 125 leaving the remainder 5 and 8 respectively, we will have to subtract 5 from 60 and 8 from 125 then we will compute the Highest Common Factor of those two number which we will get after subtracting.

a) 60 - 5 = 55

b) 125 - 8 = 117

Now, we will compute the H.C.F. of 55 and 117.

a) 55                                     b) 117

     _______                                  ________      

  5 |  55,                                     3 |  117

     |_______                                 |________

11  |  11                                      3 |   39

     |_______                                |________  

     |    1                                    13 |   13

     |                                               |________

                                                     |     1

                                                     |

1 is the only  common factor of 55 and 117. Hence H.C.F. of 55 and 117 is 1

Therefore, 1 is the largest number which divides 60 and 125 leaving the remainder of 5 and 8 respectively.

Let us check it.

a) 60 ÷ 1

Quotient = 60

Remainder = 0

b) 125 ÷ 1

Quotient = 125

Remainder = 0