Find the greatest number that divide 171 and 251 leaving 7 as a remainder .

Dear Student, 
Solution)
171 - 7 = 164 and 251 - 7 = 244
Now,
Factors of 164 = 2 × 2 × 41 and 
factors of 244 = 2 × 2 × 61
Common factors = 2 × 2
HCF of 164 and 244 = 2 × 2 = 4
Thus, the greatest number is 4.
Regards!