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.
The purpose of a factor tree is to notate the process of finding the prime factorization. If a number is already prime, a factor tree is not necessary.
a factor tree
A factor tree.
54 ^ 9x6 ^ ^ 3x3x3x2 re-write like this: 2 x 33
144 72,2 36,2,2 18,2,2,2 9,2,2,2,2 3,3,2,2,2,2
500 250,2 125,2,2 25,5,2,2 5,5,5,2,2
126 63,2 21,3,2 7,3,3,2
837 279,3 93,3,3 31,3,3,3
72 36,2 18,2,2 9,2,2,2 3,3,2,2,2
726 363,2 121,3,2 11,11,3,2
252 2x126 2x2x63 2x2x3x3x7
A factor firework is just an upside down factor tree. Write the original number at the bottom. Example: 210 7,5,3,2 35,3,2 105,2 210