Factor Tree Method

Example: 60

        60
       /    \
      6      10
     / \    /  \
    2   3  2    5

Result: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5

Division Method

Divide by smallest prime numbers repeatedly:

2 | 60
2 | 30
3 | 15
5 | 5
    1

Result: 60 = 2 × 2 × 3 × 5

Exponent Notation

Group repeated prime factors using exponents:

• 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
• 100 = 2 × 2 × 5 × 5 = 2² × 5²

Finding GCF and LCM

Prime factorization makes it easy to find the Greatest Common Factor and Least Common Multiple of numbers.

Simplifying Fractions

Use prime factors to reduce fractions to their simplest form by canceling common factors.

Cryptography

Modern encryption relies on the difficulty of factoring very large numbers into primes.

Number Theory

Foundation for understanding divisibility, modular arithmetic, and many mathematical proofs.