tests are graded… check aeries! new homework stamp logs tomorrow
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Tests are graded… Check Aeries!
New Homework Stamp Logs Tomorrow
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
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