Find the greatest number, which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.

Question: Find the greatest number, which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.Solution:The number on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.Hence, make the dividend completely divisible by the divisor. This is possible, if we subtract remainder from the dividend.Therefore,1657 - 6 = 16512037 - 5 = 2032H.C.F. of 1651 and 2032 is 127. 127 is the common factor.127 × 13 = 1651Thus by adding 6, we get 1651 + 6 = 1657127 is the correct answer.