Question

The largest no which divides 70 and 125 leaving the reminder 5 and 8 respectively .

Answer 1

Solution :-

To find the largest number which divides 70 and 125 leaving the remainder 5 and 8 respectively, we will have to subtract 5 from 70 and 8 from 125 then we will compute the Highest Common Factor of those two number which we will get after subtracting.

a) 70 - 5 = 65

b) 125 - 8 = 117

Now, we will compute the H.C.F. of 65 and 117.

 a) 65                                     b) 117
      _______                                  ________     
   5 |  65,                                     3 |  117
      |_______                                 |________
 13 |  13                                      3 |   39
      |_______                                 |________ 
      |    1                                    13 |   13
      |                                               |________
                                                      |     1
                                                      |

13 is the only common factor of 65 and 117. Hence H.C.F. of 65 and 117 is 13

Therefore, 13 is the largest number which divides 70 and 125 leaving the remainder of 5 and 8 respectively.

Let us check it.

a) 70 ÷ 13
Quotient = 5
Remainder = 5

b) 125 ÷ 13
Quotient = 9
Remainder = 8

Answer 2

Solution -

To find the largest number which exactly divides (70 - 5), and (125 - 8)

The required number is the HCF of 65 and 117
find HCF by any method. Here HCF of 65 and 117 is by Factor Method.

Factors of 65 = 1, 5, 13, 65

Factors of 117 = 1, 3, 9, 13, 39, 117

Common Factors = 1, 13

Highest Common factor (HCF) = 13 

Ans - The required number = 13

Check -

70 / 13 = 5 and remainder = 5

and 125 / 13 = 9 and remainder = 8.