+611 What is the smallest prime divisor of 5^{19} * 7^{13} * 3^{31}?
+1918 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! :)
