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Warmups

(2 3)(4 1)x x Solve the system:

4y x 3 2 7x y

(2 3) (4 1)x x

1.

2.

3.Multiply:

Subtract:

10-1 Factors and Greatest Common Factors

Objective: To find prime factorizations and greatest common factors for monomials.

Standard 11.0

Factors

Factor: a number or variable that divides evenly into your original number.

Example 1: Find the factors of 72.1 722 363 244 186 128 9This problem is like #19-23 in homework tonight!

Some terms to know

Prime: Only factors are 1 & itself Composite: Having more than 2 factors

Write the prime numbers up to 20: 1, 2, 3, 5, 7, 11, 13, 17, 19

FACTOR TREE (for composite #s)

384 2 192

2 96 2 48

2 24 2 12

2 6 2 3

2•2•2•2•2•2•2•3

Prime factorization

TOO

1) 20 2) 36 2•2•5 2•2•3•3

HintsIf it is an even, it is divisible by 2

If you add the digits and the answer is divisible by 3, then the original number is divisible by 3

If it ends in 0 or 5, it is divisible by 5

Stop trying when the answer is smaller than the number you divided by

Factoring with Variables

81b2c3

9 93 3 3 3

3•3•3•3•b•b•c•c•c

TOO32abc3

2•2•2•2•2•a•b•c•c•c

Greatest Common Factor (GCF)

Make a factor tree and multiply together what they have in common

80 282 40 2 14 2 20 2 7 2 10 2 5

2•2 = 4 =GCF

GCF: Biggest number that will divide evenly into all of the numbers

With variables, take the smallest exponent

32xy2z, 48x3y4

2•2•2•2•2, 2•2•2•2•3

GCF: 16xy2

TOO for Homework18xp2, 48x4

Challenge Problem – find the GCF

254a b 2 263a b c 3 2180ab c

9ab

254a b2 263a b c 3 2180ab c

Homework Greatest Common Factor Worksheet

Math Lab Warmups

1.

2.

3.

Multiply:

Subtract:

Write the prime factorization of the number.

Example 1: Using a Factor Tree to Find Prime Factorization

Course 2

10-1Prime Factorization

A. 2424

8 · 3

4 · 2 · 3

2 · 2 · 2 · 3

Write 24 as the product oftwo factors.

Continue factoring until allfactors are prime.

The prime factorization of 24 is 2 · 2 · 2 · 3. Usingexponents, you can write this as 23 · 3.

Write the prime factorization of the number.

Example 2: Using a Factor Tree to Find Prime Factorization

Course 2

10-1Prime Factorization

B. 150150

30 · 5

10 · 3 · 5

2 · 5 · 3 · 5

Write 150 as the productof two factors.

Continue factoring until all factors are prime.

The prime factorization of 150 is 2 · 3 · 5 · 5, or2 · 3 · 52.

Try This: Example 3

Insert Lesson Title Here

Course 2

2-4 Prime Factorization

Write the prime factorization of the number.

A. 3636

18 · 2

9 · 2 · 2

3 · 3 · 2 · 2

Write 36 as the product oftwo factors.

Continue factoring until allfactors are prime.

The prime factorization of 36 is 2 · 2 · 3 · 3. Usingexponents, you can write this as 22 · 32.

Try This: Example 4

Insert Lesson Title Here

Course 2

10-1Prime Factorization

Write the prime factorization of the number.

B. 9090

45 · 2

9 · 5 · 2

3 · 3 · 5 · 2

Write 90 as the productof two factors.

Continue factoring until all factors are prime.

The prime factorization of 90 is 3 · 3 · 5 · 2, or2 · 32 · 5.

Your turn!

Prime Factorization Worksheet

Use scratch paper to make your factor trees.

Remember to list your factors in order from least to greatest.

Work Individually

Switch and grade when everyone is done