1Cademy - Finding the GCF of $$27x^3$$ and $$18x^4$$

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Prime Factorization

Example

Finding the GCF of $27x^3$ and $18x^4$

To find the GCF of $27x^3$ and $18x^4$ , apply the prime factorization method to both the coefficients and the variables.

Step 1 — Factor coefficients and expand variables: Write $27x^3 = 3 \cdot 3 \cdot 3 \cdot x \cdot x \cdot x$ and $18x^4 = 2 \cdot 3 \cdot 3 \cdot x \cdot x \cdot x \cdot x$ .

Step 2 — Align factors in columns and circle the common ones: The shared factors are two $3$ s and three $x$ s (i.e., $3, 3, x, x, x$ ).

Step 3 — Bring down the common factors: Collect $3 \cdot 3 \cdot x \cdot x \cdot x$ .

Step 4 — Multiply: $3 \cdot 3 = 9$ and $x \cdot x \cdot x = x^3$ , giving $9x^3$ .

The GCF of $27x^3$ and $18x^4$ is $9x^3$ . This example illustrates that the GCF of expressions with variables includes the common variable factors raised to the lowest power appearing in any of the expressions.

Updated 2026-04-21

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OpenStax Elementary Algebra

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