1Cademy - Prime Factorization of 48

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Finding Prime Factorization Using a Factor Tree

Example

Prime Factorization of 48

To find the prime factorization of $48$ , begin by choosing any two factors: $48 = 2 \cdot 24$ . Since $2$ is prime, circle it. The factor $24$ is not prime, so split it: $24 = 4 \cdot 64$ . Neither $4$ nor $6$ is prime, so split each again: $4 = 2 \cdot 2$ and $6 = 2 \cdot 3$ . All resulting factors ( $2, 2, 2, 3$ ) are prime. Collecting every circled prime gives $48 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ . Starting with a different initial split, such as $48 = 6 \cdot 8$ , produces the same prime factorization, confirming that the result is unique.