Which of the following is the greatest number that divides 137 and 198 and leaves 7 and 3 as respective remainders?

Correct option is C

Given:

We need to find the greatest number that divides 137 and 198, leaving remainders 7 and 3, respectively.

Solution:

137 - 7 = 130

198 - 3 = 195

Prime factorization;

130 = 2$$\times$$5$$\times$$13

195 = 3$$\times$$​5$$\times$$​13

HCF of 130, 195 = 5$$\times$$​13 = 65 

Thus, the greatest number that divides both 137 and 198, leaving the respective remainders of 7 and 3, is 65