Question

If find the greatest number which divides 53, 79, 105 leaving reminded 5, 7,9 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