Question

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
1. 123
2. 127
3. 235
4. 305

Answer 1

Correct Answer - Option 2 : 127

Concept used:

HCF = Highest common factor 

The greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor.

Calculations:

Required number = H.C.F. of (1657 - 6) and (2037 - 5)

H.C.F. of 1651 and 2032

1651 = 13 × 127 

2032 = 4 × 4 × 127

HCF of 1651 and 2032 = 127

∴ The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is 127.