1. Using factors to find the prime factorization of a number
Factor Strings
Using factors to find the prime factorization of a number

2. Step one Here is a list of Prime Numbers;
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Divide (/) the number you want to factor by the smallest prime number on the list; 66
66 / 2
= 33

3. Step 2 = 11 Repeat the process with the smallest prime number possible
Note, 33 is not evenly divisible by 2. So, try the next smallest number – 3
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 66
66 / 2
= 33 / 3
= 11

4. Step 3
Notice that our new answer (quotient) is a prime number; 11
Once a prime number is our final quotient, we are done dividing.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 66
66 / 2
= 33 / 3
= 11

5. Step 4 Write your number string; 2 * 3 * 1166
66 / 2
= 33 / 3
= 11
2 * 3 * 11
Notice, this string is a list of the prime numbers, in order, that are multiplied (*)to get our original number; 2*3*11 = 66

6. Another Example
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
104
104 / 2
= 52 / 2
= 26 / 2
= 13
Factor String; 23 * 13 = 104
When there are more than one prime number that is the same (2 in this example), count them and use the exponent form
2 * 2 * 2 = 23