Lesson Worksheet: Factorizing Monomials Mathematics

In this worksheet, we will practice factorizing monomials completely and finding the greatest common divisor (factor) of two or more monomials.


Find the greatest common factor of 2𝑎𝑏, 𝑎𝑏, and 2𝑎𝑐, given that 𝑎, 𝑏, and 𝑐 are positive integer numbers.

  • A𝑎𝑏
  • B𝑎
  • C2𝑏
  • D2𝑎
  • E𝑏


Find the greatest common factor of 5𝑥𝑦 and 15𝑥𝑦, given that 𝑥 and 𝑦 are positive integer numbers.

  • A𝑥𝑦
  • B𝑥𝑦
  • C5𝑥𝑦
  • D15𝑥𝑦
  • E5𝑥𝑦


Find the GCF of 56𝑎𝑏 and 46𝑏, given that 𝑎 and 𝑏 are positive, whole numbers.

  • A2𝑏
  • B28𝑏
  • C28
  • D23𝑏
  • E2


A circle, 𝑀, has a radius of 2𝑎. Find the greatest common factor of its area and its circumference, given that 𝑎 is a positive integer.

  • A𝑎𝜋
  • B4𝑎𝜋
  • C𝜋
  • D2𝜋
  • E2𝑎𝜋


Completely factor the following expression: 39𝑥𝑦.

  • A133𝑥𝑥𝑦𝑦
  • B133𝑥𝑥𝑦
  • C39𝑥𝑦
  • D39𝑥𝑥𝑦𝑦
  • E133𝑥𝑦


True or False: The greatest common factor of 36𝑎𝑏𝑐 and 6𝑎𝑏𝑐 is 6𝑎𝑏𝑐.

  • AFalse
  • BTrue


Which of the following is a complete factorization of 39𝑥𝑦𝑧?

  • A3×𝑥×𝑦×𝑧
  • B39×𝑥×𝑦×𝑧
  • C3×13×𝑥×𝑦×𝑧
  • D3×3×𝑥×𝑦×𝑧
  • E13×𝑥×𝑦×𝑧


What is the greatest common factor of 30𝑎𝑏𝑐 and 6𝑎𝑏𝑐?

  • A5𝑎𝑏𝑐
  • B𝑎𝑏𝑐
  • C5𝑎𝑏𝑐
  • D6𝑎𝑏𝑐
  • E𝑎𝑏𝑐


Completely factor the following monomial: 45𝑎𝑏𝑐.

  • A45×𝑎×𝑏×𝑏×𝑐×𝑐×𝑐
  • B3×3×5×𝑎×𝑏×𝑏×𝑐×𝑐
  • C45×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐×𝑐
  • D3×5×5×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐
  • E3×3×5×𝑎×𝑏×𝑏×𝑏×𝑐×𝑐


Completely factor the following monomial: 15𝑎𝑏𝑐.

  • A3×5×𝑎×𝑏×𝑏×𝑏×𝑐×𝑐
  • B3×5×𝑎×𝑏×𝑏×𝑐×𝑐
  • C15×𝑎×𝑏×𝑏×𝑐×𝑐
  • D3×5×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐
  • E15×𝑎×𝑎×𝑏×𝑏×𝑐×𝑐

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