Chapter 9.1

Factoring a number  Objective NCSCOS 1.01 – Write equivalent forms of algebraic expressions to solve problems  Students will know how to factor number and find the greatest common factor

Factoring a number  Prime number –  A number that can only be divided by 1 and itself  Ex. 2, 3, 5, 7, 11, 13  Composite number –  A number that can be divided by more than 1 and itself  Ex. 4: (1*4, 2*2)  Ex. 6: (1*6, 2*3)

Factoring a number  Prime Factorization –  A composite number expressed as a product of factors that are all prime numbers  The process of factoring a number down to only prime numbers

Factoring a number  Label the following as prime or composite  24  23  18  9  53

Factoring a number  Label the following as prime or composite  24  23  18  9  53 Composite Prime Composite Prime

Factoring a number  Example 1: Find the prime factorization of 90  The smallest prime number is 2, so we start with 2  When you take a 2 out, you’re left with 45

Factoring a number  Example 1: Find the prime factorization of 90  The two numbers below 90 should multiply to the number above it  2 can’t be factored any more, so we’ll have to factor the 45 more x = 90

Factoring a number  Example 1: Find the prime factorization of 90  The next smallest prime number is 3, so take 3 out of 45  Notice that 3 and 15 multiply to the number above it x = 45

Factoring a number  Example 1: Find the prime factorization of 90  15 can be factored by 3 again  At this point, all the number are prime

Factoring a number  Example 1: Find the prime factorization of 90  We can multiply all these numbers together to get 90

Factoring a number  Example 1: Find the prime factorization of 90  We can then write 3 * 3 as 3 2  We now have 90 fully factored

Factoring a number  Example 2: Factor -28  If it’s negative, factor out -1 first  Now factor a positive 28

Factoring a number  Factor the following numbers:

Factoring a number  Factor the following numbers: * 3 * 5 * * * * 2 * 5 * * 3 * 7

Factoring a number  Example 3: Factor  Factor the number first

Factoring a number  Example 3: Factor  Then factor the variable  Remember, x 3 is x*x*x

Factoring a number  Example 3: Factor  We can now reduce this to get our answer

Factoring a number  Factor the following: 1. 20x x x 4 y x 3 y x 5

Factoring a number  Factor the following: 1. 20x x x 4 y x 3 y x * 5 * x * x 5 -1 * 2 3 * 3 * 5 * x * 17 * x 3 * y * 3 3 * 7 * x 4 *y 2

Factoring a number  Example 4:Find the Greatest Common Factor of :  We need to factor both numbers first and

Factoring a number  Factor 24

Factoring a number  Factor 36

Factoring a number  Write out each numbers factors  Find what they have in common  Multiply what they have in common to find the Greatest Common Factor GCF

Factoring a number  Find the GCF for:  Factor each number first  Find what they have in common and

Factoring a number  Find the GCF for:  Factor each number first  Find what they have in common and

Factoring a number  Find the GCF for:  You have to factor the numbers to find the GCF but you can use a shortcut for the variables:  Which value of x has the lowest number as an exponent will be your GCF and

Factoring a number  Find the Greatest Common Factor for the following: and and x 3 and 90x x 5 and 468x x 4 and 104x 4

Factoring a number  Find the Greatest Common Factor for the following: and and x 3 and 90x 5 18x x x 4 and 104x x 5 and 468x 7 156x 5

Factoring a number  Example: Find the GCF for the following numbers:  First, factor out each number

Factoring a number  Find what they have in common  They all have one 2  They also have one 3

Factoring a number  Multiply the numbers  Find the smallest value of x and plug it in

Factoring a number  Example: Find the GCF for the following numbers:  The answer is:

Factoring a number  Factor: 252  Factor: -594x 2 y 4  Find the greatest common factor:  48 and 120  84x 5 and 112x 3  117x 7, 468x 4 and 351x 5

Factoring a number  Factor: 252  Factor: -594x 2 y 4  Find the greatest common factor:  48 and 120  84x 5 and 112x 3  117x 7, 468x 4 and 351x *3 2 *7 -1*2*3 3 *11*x 2 *y x 3 117x 4