Number theory

Let's list our all the factors of each number and find if we have any common divisors. 

The factors of 123451 are $1, 41, 3011, 123451$

The factors of 708677 are $1, 367, 1931, 708677$

As shown, the only common factor shared by the 2 numbers are 1. 

Thus, the GCF is just $1$

So our final answer is 1. 

Thanks! :)