6.1.4 Prime Factorization

Vocabulary Factor – Any number in a multiplication expression examples: 5 is a factor of 10 4 is a factor of 28 Prime Number – Whole number greater than 1 with only two factors: 1 and itself examples: 11 is a prime number 23 is a prime number Composite – Whole number greater than 1 that isn’t a prime number (hint: because it is a composite of factors, it is comprised of factors) examples: 15 is a composite (5 x 3) 28 is a composite (7 x 4)

Vocabulary Factor Pair – The pair of multiplied factors that create a product examples: 2 and 5 are a factor pair of 10 7 and 3 are a factor pair of 21 Factor Tree – A diagram (looks like tree branches) used to find all the factors of a composite

Factor Tree Examples

Prime Factorization Prime Factorization Prime Factorization – All the prime factors that when multiplied create the product Prime Factorization

Writing a Prime Factorization Step #1: Choose any factor pair of the composite to begin the factor tree example: 48 2 · 24 Step #2: Continue to find factors until each branch ends at a prime number; circle prime numbers as you find them 2 · 12 4 · 3 2 · 2

Writing a Prime Factorization Step #3: Write out all the prime numbers in a single line in the order they appear in the tree example: The prime factorization of 48 is 2· 2· 3· 2· 2 (but it doesn’t make sense to write 2· 2 when we know a simpler way to write it, so…) Step #4: Simplify the prime number list to exponents where you can The prime factorization of 48 is 2⁴ · 3

Using Prime Factorization Remember perfect squares? (The product of a number multiplied by itself) Examples: 9, 16, 49, 64, 25 Well, what if you’re asked to find all the perfect square factors of a really large number, like 1575 ?? Use prime factorization to solve difficult tasks. Step #1: If you look at the last two digits of the number, you can see that it’s 75. You know that 25 divides into 75, so the first factor in your number tree should be 25.

Using Prime Factorization Step #2: To find out the factor pair, divide 1575 by 25 and you get 63 example: 1575 25 · 63 Step #3: Continue with the prime factorization as you would with any other number 25 · 63 5 · 5 7 · 9 3 · 3 Step #4: The prime factorization shows there are THREE numbers that are perfect squares: 25, 9, and 225 (3 x 5)· (3 x 5) = 15· 15 = 225

Homework Page 28: (#8, 9, 12, 13, 16, 17, 18, 21, 24, 26, 27)