Question 107997
To determine if a number is prime, divide it by all of the prime numbers less than the square root of the number. If none of the prime divisors divides the number evenly, then then number is prime.

{{{sqrt(345)}}} is a little more than 18, so you have to divide by:

2, 3, 5, 7, 11, 13, and 17.  


The number 345 is odd, so 2 is not a factor.

{{{345/3=115}}}, so 3 is a factor, and 345 is composite.


2 wasn't a factor of 345, so it can't be a factor of 115 either.

{{{115/3}}} is not integral, so 345 only has the single 3 as a factor.

{{{115/5=23}}}, so 5 is another factor of 345.

And finally, 23 is prime because it is not divisible by either 2  or 3 ({{{sqrt(23)<5}}})


Therefore, the prime factorization of 345 is (3 * 5 * 23)