Practice Objectives
- Demonstrate the ability to find the prime factorization of a number
- Demonstrate the ability to find the GCF for a group of numbers
- Demonstrate the ability to find the GCF for a group of variable expressions
- Demonstrate the ability to find the GCF for a group of monomials
Practice Finding the Greatest Common Factor (GCF) for a Group of Monomials
Instructions:
Answer 7/10 questions correctly to pass.
Find the Greatest Common Factor (GCF) for each group of monomials.
Formatting Notes:
- Use the "^" key for exponents when typing your answer
- Your input will display with proper formatting
- x^9 » x9
- Exponents can only be used with variables (not numbers)
- Simplify numerical exponents before entering your answer
- x9 ✔
- 29 ❌ (Numerical exponents must be simplified)
- Exponents must be single-digit positive integers (1 - 9) only
- x9 ✔
- x12 ❌
- x0 ❌
- Writing an exponent of 1 or a coefficient of 1 is optional
- x1 = x
- 1x3 = x3
- Coefficients must be placed directly in front of any variable expression
- 3x ✔
- x3 ❌
- If a variable appears more than once, write in exponent form
- xxyz = x2yz
- xyxzyz = x2y2z2
- Allowed variables are x, y, and z only
Problem:
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Finding the Greatest Common Factor for Monomials:
- Number Part:
- Find the prime factorization of each number
- Build a list of all prime factors that are common to ALL monomials
- Apply the appropriate exponent to each prime factor in the list
- Use the exponent that represents the least number of occurrences of the prime factor across all of the prime factorizations
- Find the product of the prime factors in the list raised to the correct exponents, this is the number part of the GCF
- If there are no prime factors in common to ALL, the GCF is 1
- Variable Part:
- Identify which variables are present in ALL monomials
- For each common variable, choose the smallest exponent of that variable that appears across all the monomials
- If there are no variables in common to ALL, the GCF is 1
- The GCF is the product of the number part and the variable part
Step-by-Step:
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