Questions and Answers
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?
a number that has no factors other than one and itself
What is the prime factorization of 210?
235*7
What is the GCF of -10c^2 d and 15cd^2?
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What is the GCF of 38m and 57n?
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What is the GCF of 56 and 46?
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What is the GCF of 48 and 60?
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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?
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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?
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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?
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What is the GCF of the polynomial 8x^6y^5 - 3x^8y^3?
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What is the importance of variable expressions?
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How can prime factorization be used?
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What is the GCF of two or more monomials?
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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.
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