Algebra I: Greatest Common Factor Quiz

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Questions and Answers

What is a prime number?

A number that has no factors other than one and itself.

What is the Greatest Common Factor (GCF)?

The largest whole number that will divide a group of whole numbers without remainders.

What is the GCF of 56 and 46?

2

What is the prime factorization of 210?

<p>2 X 3 X 5 X 7</p> Signup and view all the answers

What is the GCF of 170 and 210?

<p>10</p> Signup and view all the answers

What is the GCF of 25 · 5 · 11 and 23 · 5 · 7?

<p>5</p> Signup and view all the answers

What is the GCF of 48 and 60?

<p>12</p> Signup and view all the answers

What is the GCF of the literal terms m7n4p3 and mn12p5?

<p>m1n4p3</p> Signup and view all the answers

What is the GCF of the literal terms xxyyyzz and xxxxzzz?

<p>x2z2</p> Signup and view all the answers

What are the exponents for the variables of the GCF of the monomials 9x2y2 and 5x2y3?

<p>x2y2</p> Signup and view all the answers

What is the GCF of the monomials -50m4n7 and 40m2n10?

<p>10m2n7</p> Signup and view all the answers

What is the GCF of -10c2d and 15cd2?

<p>5cd</p> Signup and view all the answers

What is the GCF of 38m and 57n?

<p>19</p> Signup and view all the answers

What is the GCF of the polynomial 8x6y5 - 3x8y3?

<p>x6y3</p> Signup and view all the answers

What is the GCF of the polynomial 16a4b4 + 32a3b5 - 48a2b6?

<p>16a2b4</p> Signup and view all the answers

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Study Notes

Prime Numbers

  • Defined as numbers that have no divisors other than one and themselves.

Greatest Common Factor (GCF)

  • The GCF is the largest whole number that divides a set of whole numbers without leaving a remainder.

GCF Examples

  • GCF of 56 and 46 is 2.
  • GCF of 170 and 210 is 10.

Prime Factorization

  • The prime factorization of 210 is expressed as 2 × 3 × 5 × 7.

GCF of Literal Terms

  • GCF of m7n4p3 and mn12p5 is m1n4p3.
  • GCF of xxyyyzz and xxxxzzz is x2z2.
  • GCF of 9x2y2 and 5x2y3 is represented with exponents as x2y2.

GCF of Monomials

  • For -50m4n7 and 40m2n10, the GCF is 10m2n7.
  • For -10c2d and 15cd2, the GCF is 5cd.
  • GCF of 38m and 57n is 19.

GCF of Polynomials

  • GCF of the polynomial 8x6y5 - 3x8y3 is x6y3.
  • GCF of the polynomial 16a4b4 + 32a3b5 - 48a2b6 is 16a2b4.

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