Example

Finding the GCF of 14x314x^3, 70x270x^2, and 105x105x

To find the greatest common factor of 14x314x^3, 70x270x^2, and 105x105x, use the prime factorization method.

Step 1 — Factor coefficients and expand variables: Write 14x3=27xxx14x^3 = 2 \cdot 7 \cdot x \cdot x \cdot x, 70x2=257xx70x^2 = 2 \cdot 5 \cdot 7 \cdot x \cdot x, and 105x=357x105x = 3 \cdot 5 \cdot 7 \cdot x.

Step 2 — Align factors in columns and circle the common ones: The shared factors across all three terms are one 77 and one xx (i.e., 7,x7, x).

Step 3 — Bring down the common factors: Collect 7x7 \cdot x.

Step 4 — Multiply: 7x=7x7 \cdot x = 7x.

The GCF of 14x314x^3, 70x270x^2, and 105x105x is 7x7x.

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Updated 2026-04-29

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