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Questions and Answers
What is the greatest common factor?
What is the greatest common factor?
the largest whole number that will divide a group of whole numbers without remainders
What is a prime number?
What is a prime number?
a number that has no factors other than one and itself
What is the prime factorization of 210?
What is the prime factorization of 210?
235*7
What is the GCF of -10c^2 d and 15cd^2?
What is the GCF of -10c^2 d and 15cd^2?
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What is the GCF of 38m and 57n?
What is the GCF of 38m and 57n?
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What is the GCF of 56 and 46?
What is the GCF of 56 and 46?
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What is the GCF of 48 and 60?
What is the GCF of 48 and 60?
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What is the GCF of 170 and 210?
What is the GCF of 170 and 210?
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What is the GCF of the polynomial 16a^4b^4 + 32a^3b^5 - 48a^2b^6?
What is the GCF of the polynomial 16a^4b^4 + 32a^3b^5 - 48a^2b^6?
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What is the GCF of 2^5, 5, 11 and 23, 52, 7?
What is the GCF of 2^5, 5, 11 and 23, 52, 7?
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What are the exponents for the variables of the GCF of 9x^2 y^2 and 5x^2 y^3?
What are the exponents for the variables of the GCF of 9x^2 y^2 and 5x^2 y^3?
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What is the GCF of -50m^4 n^7 and 40m^2 n^10?
What is the GCF of -50m^4 n^7 and 40m^2 n^10?
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What is the GCF of xxyyyzz and xxxxzzz?
What is the GCF of xxyyyzz and xxxxzzz?
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What is the GCF of the polynomial 8x^6y^5 - 3x^8y^3?
What is the GCF of the polynomial 8x^6y^5 - 3x^8y^3?
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What is the importance of variable expressions?
What is the importance of variable expressions?
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How can prime factorization be used?
How can prime factorization be used?
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What is the GCF of two or more monomials?
What is the GCF of two or more monomials?
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What is the GCF of a polynomial?
What is the GCF of a polynomial?
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Study Notes
Greatest Common Factor (GCF)
- The GCF is the largest whole number that divides a group of whole numbers without leaving a remainder.
- It can be determined through methods such as prime factorization.
Prime Numbers
- A prime number is defined as a number greater than one that has no positive divisors other than one and itself.
Prime Factorization Examples
- The prime factorization of 210 is found to be 2 × 3 × 5 × 7.
GCF Calculations
- For the terms -10c²d and 15cd², the GCF is -5c²d².
- The GCF of 38m and 57n is calculated to be 19mn.
- The GCF of the integers 56 and 46 results in 2.
- For the numbers 48 and 60, the GCF is established as 12.
- The GCF for 170 and 210 is obtained as 10.
GCF of Polynomials
- For the polynomial 16a⁴b⁴ + 32a³b⁵ - 48a²b⁶, the GCF is 16a²b⁴.
- The GCF for the monomials 9x²y² and 5x²y³ results in x²y².
- In the case of -50m⁴n⁷ and 40m²n¹⁰, the GCF is 5m²n⁷.
- The GCF from the polynomial 8x⁶y⁵ - 3x⁸y³ is determined to be x⁶y³.
GCF of Literal Terms
- For the literal terms xxyyyzz and xxxxzzz, the GCF is x²z².
- The GCF of the literal terms m⁷n⁴p³ and mn¹²p⁵ results in mn⁴p³.
Review Points
- Variable expressions abide by the properties of real numbers.
- Prime factorization serves as a technique for determining the GCF of whole numbers and monomials.
- The GCF of monomials is the product of the greatest shared numerical and variable factors.
- For polynomials, the GCF is the GCF of its constituent terms.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of the Greatest Common Factor with these flashcards. Each card includes key definitions and examples to help you understand the concepts of GCF and prime factorization. Ideal for algebra students looking to enhance their learning.
