# Prime Factorization

 There are different methods which can be utilized to find the prime factorization of a number. One way is to repeatedly divide by prime numbers: EXAMPLE   1.   Prime factorization of 96 (by division): 96 ÷ 2 = 48     48 ÷ 2 = 24         24 ÷ 2 = 12             12 ÷ 2 = 6                 6 ÷ 2 = 3                     3 ÷ 3 = 1 96 = 2 * 2 * 2 * 2 * 2 * 3 EXAMPLE   2.   Prime factorization of 120 (by division): 120 ÷ 2 = 60     60 ÷ 2 = 30         30 ÷ 2 = 15             15 ÷ 3 = 5                 5 ÷ 5 = 1 120 = 2 * 2 * 2 * 3 * 5 Another way to approach the task is to choose ANY pair of factors and split these factors until all the factors are prime:  Traditionally, the factors are listed in order from least to greatest. While the product would be the same regardless of the order of the factors, it is much easier to compare or evaluate expressions if the factors are listed in this order. Determining the prime factors can be challenging. While it's good to know HOW to do it, on most standardized tests you'll only have to select the one right answer choice to show that you understand the concept. The CORRECT answer:         must be only PRIME numbers         must multiply together to give the specified quantity. Sample #1: Which shows the prime factorization of 30? A) 2 * 15 B) 3 * 10 C) 2 * 3 * 5 D) 2 * 2 * 3 * 5 Check your answer 30=6x5 30=2x3x5 choice (C) Remember, use any of the methods to calculate the prime factorization (on multiple choice tests, you may also 'work backwards' from the answers -- trying each until one is found that meets BOTH rules). The Prime Factorization MUST: Be ONLY prime numbers and produce the CORRECT PRODUCT. PRACTICE QUESTIONS Exercise #1: Which shows the prime factorization of 36? A) 2 * 2 * 3 * 3 B) 2 * 3 * 3 * 3 C) 2 * 18 D) 3 * 12 Check your answer 36=2x18 (or 3x12) 36=4x9 (or 6x6) 30=2x2x3x3 choice (A) Exercise #2: Which shows the prime factorization of 63? A) 2 * 3 * 21 B) 7 * 9 C) 3 * 21 D) 3 * 3 * 7 Check your answer 63=9x7 (or 3x21) 63=3x3x7 choice (D) Exercise #3: Which shows the prime factorization of 67? A) 1 * 67 B) 3 * 17 C) 3 * 19 D) 7 * 19 Check your answer 67 is prime 67=1x67 choice (A) Exercise #4: Which shows the prime factorization of 70? A) 7 * 10 B) 5 * 14 C) 2 * 5 * 7 D) 2 * 2 * 5 * 7 Check your answer 70=2x35 (or 5x14) 30=2x5x7 choice (C) Exercise #5: Which shows the prime factorization of 78? A) 2 * 2 * 3 * 7 B) 2 * 3 * 13 C) 2 * 3 * 17 D) 2 * 39 Check your answer 78=6x13 (or 2x39) 30=2x3x13 choice (B) Exercise #6: Which shows the prime factorization of 84? A) 7 * 12 B) 4 * 21 C) 2 * 2 * 3 * 3 * 7 D) 2 * 2 * 3 * 7 Check your answer 84=12x7 (or 4x21) 84=2x2x3x7 choice (D) Exercise #7: Which shows the prime factorization of 91? A) 1 * 91 B) 3 * 29 C) 7 * 13 D) 13 * 17 Check your answer 91=7x13 choice (C) Answers 1)   A 2)   D 3)   A 4)   C 5)   B 6)   D 7)   C