Question

find the greatest number that can divide 166 and 237 leaving remainders 5 and 7 respectively.

Answer 1

166-5=161
237-7=230
Find hcf of 161 and 230
The hcf of 161 and 230 is 23
So answer is 23

Answer 2

Given number - 166 and 237

Remainder = 5 and 7 respectively

Now,  

166 - 5 = 161 = 7 * 23

237 - 7 = 230 = 5 * 2 * 23

H. C. F. = 23

Hence, the number is 23