What is the smallest prime divisor of 5^{19} * 7^{13} * 3^{31}?

1 answer

The prime factorization of the given number is:

5^{19} * 7^{13} * 3^{31}

To find the smallest prime divisor of this number, we need to find the smallest prime number that divides into this number without any remainder.

Since each of the numbers (5, 7, and 3) are prime numbers themselves, the smallest prime divisor of this number would be the smallest prime number involved in this expression, which is 3.

Therefore, the smallest prime divisor of the given number is 3.