Prime Factorization
Prime factorization breaks a number all the way down until every piece is a prime.
This is a free explanation of Prime Factorization — a preview, not the full interactive lesson. The lesson, practice, quizzes, and AI Tutor are inside the app.
A prime number is any whole number greater than 1 that is only divisible by 1 and itself — like 2, 3, 5, 7, 11, 13. Numbers with other factors (like 4 = 2 × 2, or 12 = 3 × 4) are composite. Prime factorization means breaking a number down until every piece is a prime — no composite pieces left.
The easiest method is the factor tree: pick any two factors of your number, then keep breaking down any factor that isn’t prime yet, until every branch ends in a prime number. The result is always the same no matter which starting factors you pick.
Once a number is fully factored, you can write repeated primes with exponents. Prime factorization is also the fast route to the GCF and LCM for larger numbers.
Worked example
Find the prime factorization of 48.
- Start with any two factors: 48 = 6 × 8.
- Break down each composite piece: 6 = 2 × 3 (both prime), and 8 = 2 × 4, then 4 = 2 × 2.
- Collect all the primes at the ends of the branches: 48 = 2 × 2 × 2 × 2 × 3.
- Using exponents, that is 2⁴ × 3.
48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3
On the test: Prime factorization powers the GCF and LCM methods used throughout Basic Math and algebra.
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- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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