Intro to Factoring: Finding and Using the GCF

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Date: _________________________

Part 1: GCF of Integers (Basic)

Instructions: Find the greatest common factor (GCF) for each pair or group of numbers.

  1. 12 and 18
  2. 20 and 45
  3. 32 and 48
  4. 15 and 28
  5. 42 and 56
  6. 9, 27, and 36

Part 2: GCF of Variable Terms

Instructions: Find the greatest common factor (GCF) for each pair or group of variable terms. Hint: For variables, the GCF is the lowest power that appears in every term.

  1. $x^3$ and $x^5$
  2. $y^2$ and $y^7$
  3. $a^4$, $a^2$, and $a^8$
  4. $m^3n^2$ and $m^5n$
  5. $p^2q^3$ and $p^4q^2$
  6. $c^3d^2$, $cd^4$, and $c^2d$

Part 3: GCF of Monomials (Intermediate)

Instructions: Find the greatest common factor (GCF) for each group of monomials by combining the skills from Part 1 and Part 2.

  1. $5x$ and $10$
  2. $12y^2$ and $18y^3$
  3. $14a^3$ and $21a$
  4. $20m^4$ and $50m^2$
  5. $8x^2y$ and $24xy^3$
  6. $15a^3b^2$, $25a^2b^4$, and $5ab^3$

Part 4: Factoring the GCF from Polynomials (Intermediate)

Instructions: First, find the GCF of all terms in the polynomial. Then, factor it out. Write your answer in the form GCF(remaining terms).

  1. $7x + 21$
  2. $10y^2 - 15y$
  3. $8a^3 + 12a^2$
  4. $16b^5 - 32b^3$
  5. $9m^2n + 12mn^2$
  6. $6x^3y^2 - 18x^2y^3 + 24xy$