All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
If the factorization includes the number 2, it's even. If not, it's odd.
If the prime factorization contains a 5 and a 7, 35 is a factor.
Very easily: if the prime factorization includes 2, it's even. If not, it's odd.
The factorization of a number is a series of numbers that make that number 
the prime factorization of 56 is a prime number that are only divisible by twounique factors.
Given the prime factorization of an integer how can you determine if our integer is a perfect square?
33
The only number with that prime factorization has to be 48.
A prime number has only 2 factors which are itself and one whereas a composite number has more than two factors.
A factor rainbow is a method to determine a prime factorization.
The prime number is the prime factorization. For example, the prime factorization of the prime number 3 is 3. Get it?
Prime factorization of the number 54 is 2 x 33.