Question

Find the greatest number, which on dividing 107 and 120 leaves remainders 5 and 1, respectively.

Answer 1

Solution :-

To find the greatest number, which on dividing 107 and 120 leaves remainders 5 and 1 respectively, first we will subtract 5 from 107 and 1 from 120.

107 - 5 = 102

120 - 1 = 119

Now, we will find the H.C.F. of 102 and 119

Prime factorization of 102 = 2 × 3 × 17

Prime factorization of 119 = 7 × 17

17 is the only common factor of 102 and 119

So, H.C.F. of 102 and 119 is 17

So, 17 is the greatest number which on dividing 107 and 120, leaves remainders 5 and 1 respectively.

We can check our answer.

107 ÷ 17 

Quotient = 6 and Remainder = 5

120 ÷ 17

Quotient = 7 and Remainder = 1
  
So, the answer is correct.