Lesson Worksheet: Greatest Common Factor of Monomials Mathematics • 7th Grade

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

Q1:

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

  • A2𝑏
  • B28𝑏
  • C28
  • D23𝑏
  • E2

Q2:

Find the GCF of 27𝑎 and 15𝑎𝑏, given that 𝑎 and 𝑏 are positive, whole numbers.

  • A3𝑎
  • B9𝑎
  • C9
  • D5𝑎
  • E3

Q3:

Find the GCF of 62𝑎𝑏 and 36𝑏, given that 𝑎 and 𝑏 are positive, whole numbers.

  • A2𝑏
  • B31𝑏
  • C31
  • D18𝑏
  • E2

Q4:

Consider the rectangle shown.

Find its area.

  • A12𝑎
  • B8𝑎
  • C16𝑎
  • D8𝑎
  • E12𝑎

Find its perimeter.

  • A12𝑎
  • B12𝑎
  • C8𝑎
  • D16𝑎
  • E8𝑎

Find the greatest common factor of the area and the perimeter.

  • A2𝑎
  • B2𝑎
  • C8𝑎
  • D4𝑎
  • E4𝑎

Q5:

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

  • A𝑥𝑦
  • B𝑥𝑦
  • C5𝑥𝑦
  • D15𝑥𝑦
  • E5𝑥𝑦

Q6:

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

Q7:

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

  • A5𝑎𝑏𝑐
  • B𝑎𝑏𝑐
  • C5𝑎𝑏𝑐
  • D6𝑎𝑏𝑐
  • E𝑎𝑏𝑐

Q8:

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

Q9:

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

  • AFalse
  • BTrue

Q10:

True or False: The greatest common factor of monomials is the product of their common prime factors.

  • AFalse
  • BTrue

Q11:

If the greatest common factor of two monomials is 2𝑥𝑦 and one of the monomials is 4𝑥𝑦, which of the following is the other monomial?

  • A8𝑥𝑦
  • B6𝑥𝑦
  • C6𝑥𝑦
  • D2𝑥𝑦
  • E8𝑥𝑦

Q12:

If the greatest common factor of two monomials is 2𝑎𝑏𝑐 and one of the monomials is 6𝑎𝑏𝑐, which of the following could be the other monomial?

  • A3𝑎𝑏𝑐
  • B𝑎𝑏𝑐
  • C𝑎𝑏𝑐
  • D40𝑎𝑏𝑐
  • E6𝑎𝑏𝑐

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