1Cademy - Finding the GCF of 54 and 36

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Prime Factorization

Example

Finding the GCF of 54 and 36

To find the GCF of $54$ and $36$ , apply the four-step prime factorization method.

Step 1 — Factor into primes: Use factor trees to find $54 = 2 \cdot 3 \cdot 3 \cdot 3$ and $36 = 2 \cdot 2 \cdot 3 \cdot 3$ .

Step 2 — Align and circle common factors: Arrange the prime factors in columns and circle the factors shared by both numbers. The common factors are one $2$ , one $3$ , and another $3$ .

Step 3 — Bring down the common factors: Collect $2, 3, 3$ .

Step 4 — Multiply: $2 \cdot 3 \cdot 3 = 18$ .

The GCF of $54$ and $36$ is $18$ . Because the GCF is a factor of both numbers, each can be written as a multiple of $18$ : $54 = 18 \cdot 3$ and $36 = 18 \cdot 2$ .