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

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

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

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

Step 4 Write your number string; 2 * 3 * 11 66 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

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