Number Theory

Let's list out every single factor for each number and identify the factors they share. 

We find that

The factors of 294343 are \(1, 7, 49, 6007, 42049, 294343\)

The factors of 878568 are \(1, 2, 3, 4, 6, 8, 12, 24, 36607, 73214, 109821, 146428, 219642, 292856, 439284, 878568\)

 

As shown, the only common factor between the two is 1. 

Now, we could also use Euclid's algorithm or prime factorization, but the GCF is just 1. 

 

So our final answer is 1. 

 

Thanks! :)