#1**+1 **

The smallest possible prime divisor a number can have is of course, 2

If we check the multiplication, we can see that 3 odd numbers can't possibly mulitply to be an even.

So, \(5^{19} * 7^{13} * 3^{31}\) is not divisble by 2.

The next smallest is 3.

The third term of the multiplication is \(3^{31 }\)

This means, no matter what, this number has to be divisible by 3, since 3 is part of the factorization, meaning it is a factor. .

So 3 is our final answer.

Thanks! :)

NotThatSmart Aug 26, 2024