The sum of two positive integers $a$ and $b$ is 1001.  What is the largest possible value of $\gcd(a,b)$?
Question:
The sum of two positive integers $a$ and $b$ is 1001.  What is the largest possible value of $\gcd(a,b)$?
Answer:
Let's think step by step.

user
143
The sum of two positive integers $a$ and $b$ is 1001.  What is the largest possible value of $\gcd(a,b)$?
train