INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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### Special Product

• Recall the concepts of prime factor, composite factor, and the prime factorization of a number from your earlier work.
• A monomial is in factored form if it is expressed as a product of prime numbers and variables, and no variable has an exponent greater than 1.
• The greatest common factor (GCF) of 2 or more monomials is the product of their common factors.

### Special Product

Write in prime factored form: 400
• 400 = 40 ×10
• 8 ×5 ×2 ×5
• 2 ×2 ×2 ×5 ×2 ×5
2 ×2 ×2 ×2 ×5 ×5
Write in prime factored form: 224
• 224 = 4 ×56
• 2 ×2 ×8 ×7
2 ×2 ×2 ×2 ×2 ×7
Write in prime factored form: 144
• 144 = 12 ×12
• 3 ×4 ×3 ×4
• 3 ×2 ×2 ×3 ×2 ×2
2 ×2 ×2 ×2 ×3 ×3
Write in factored form:
196a4b3c
• 4 ×49 ×a ×a ×a ×a ×b ×b ×b ×c
2 ×2 ×7 ×7 ×a ×a ×a ×a ×b ×b ×b ×c
Write in factored form:
175g2hi5
• 25 ×7 ×g ×g ×h ×i ×i ×i ×i ×i
5 ×5 ×7 ×g ×g ×h ×i ×i ×i ×i ×i
Write in factored form:
48u2v3w
• 4 ×12 ×u ×u ×v ×v ×v ×w
• 2 ×2 ×3 ×4 ×u ×u ×v ×v ×v ×w
2 ×2 ×2 ×2 ×3 ×u ×u ×v ×v ×v ×w
Find the GCF of 24, 60, and 72
• 24 = 2 ×2 ×2 ×3
• 60 = 5 ×12 = 2 ×2 ×3 ×5
• 72 = 6 ×12 = 2 ×3 ×2 ×2 ×3 = 2 ×2 ×2 ×3 ×3
• 24 = 2 ×60 = 5 ×12 = ×572 = 6 ×12 = 2 ×3 ×2 ×2 ×3 = 2 ××3
GCF = 2 ×2 ×3 = 12
Find the GCF of 36, 50, and 92
• 36 = 6 ×6 = 2 ×2 ×3 ×3
• 50 = 2 ×25 = 2 ×5 ×5
• 92 = 2 ×46 = 2 ×2 ×23
• 36 = 6 ×6 = ×2 ×3 ×350 = 2 ×25 = ×5 ×592 = 2 ×46 = ×2 ×23
GCF = 2
Find the GCF of:
12x2y2, 18xy3, 72x3y
• 12x2y2 = 2 ×2 ×3 ×x ×x ×y ×y
• 18xy3 = 2 ×9 = 2 ×3 ×3 ×x ×y ×y ×y
• 72x3y = 6 ×12 = 2 ×3 ×2 ×2 ×3 = 2 ×2 ×2 ×3 ×3 ×x ×x ×x ×y
• 12x2y2 = ×2 ×××x ××y18xy3 = 2 ×9 = ××3 ×××y ×y72x3y = 6 ×12 = 2 ×3 ×2 ×2 ×3 = ×2 ×2 ××3 ××x ×x ×
• 2 ×3 ×x ×y
GCF = 6xy
Find the GCF of:
16g5h3i, 36g2h3i4, 48g3h2i4
• 16g5h3i = 2 ×8 = 2 ×2 ×2 ×2 ×g ×g ×g ×g ×g ×h ×h ×h ×i
• 36g2h3i4 = 3 ×12 = 3 ×3 ×2 ×2 = g ×g ×h ×h ×h ×i ×i ×i ×i
• 48g3h2i4 = 4 ×12 = 2 ×2 ×2 ×2 ×3 ×g ×g ×g ×h ×h ×i ×i ×i ×i
• 16g5h3i = 2 ×8 = ××2 ×2 ××g ×g ×g ××h ×36g2h3i4 = 3 ×12 = 3 ×3 ×× = ××h ××i ×i ×i48g3h2i4 = 4 ×12 = ××2 ×2 ×3 ××g ×××i ×i ×i
• 2 ×2 ×g ×g ×h ×h ×i
4g2h2i

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Special Product

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Prime and Composite Numbers 0:09
• Prime Number
• Composite Number
• Factored Forms 1:39
• Prime Factored Form
• Factored Form
• Greatest Common Factor 3:55
• Example: GCF for Number
• Example: GCF for Monomial
• Example 1: Prime Factored Form 7:51
• Example 2: Factored Form 9:34
• Example 3: GCF 11:12
• Example 4: GCF 13:28