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.

Q1:

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

Q2:

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

  • A𝑥𝑦
  • B𝑥𝑦
  • C5𝑥𝑦
  • D15𝑥𝑦
  • E5𝑥𝑦

Q3:

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

  • A2𝑏
  • B28𝑏
  • C28
  • D23𝑏
  • E2

Q4:

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

Q5:

Completely factor the following expression: 39𝑥𝑦.

  • A133𝑥𝑥𝑦𝑦
  • B133𝑥𝑥𝑦
  • C39𝑥𝑦
  • D39𝑥𝑥𝑦𝑦
  • E133𝑥𝑦

Q6:

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

  • AFalse
  • BTrue

Q7:

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

Q8:

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

  • A5𝑎𝑏𝑐
  • B𝑎𝑏𝑐
  • C5𝑎𝑏𝑐
  • D6𝑎𝑏𝑐
  • E𝑎𝑏𝑐

Q9:

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

Q10:

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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