Greatest Common Factor Factoring Practice Test

Identify the greatest common monomial and factor it from algebraic expressions completely.

Greatest Common Factor Factoring Practice Test

20 questions on numerical and variable greatest common factors.

About This Greatest Common Factor Factoring Practice Test

Factoring the GCF is the first step to check before using any other polynomial factoring method.

Questions include coefficient gcds, minimum variable exponents, negative leading terms, three-term polynomials, and checking whether a GCF factorization is complete.

Skills Covered

You will find gcds of coefficients, select the smallest shared variable exponents, factor negative GCFs, divide each term accurately, and recognize incomplete factorizations.

How to Approach the Questions

  1. Find the greatest numerical divisor of all coefficients.
  2. For each shared variable, use the smallest exponent appearing in any term.
  3. Divide every term by the full GCF.
  4. Check the expression inside parentheses for any remaining common factor.

Common Mistakes to Avoid

Typical errors include taking a common factor that is not greatest, using the largest variable exponent, losing a sign, or leaving another common factor inside the parentheses.

Practice Format

Use this free 20-question test for classroom review, tutoring, homework support, exam preparation, or independent practice. Each response is followed by an explanation, and the test can be repeated without registration.