Prime Factorization Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Find the prime factorization of 360360 using a factor tree.

Solution

  1. 1
    Start: 360=2×180360 = 2 \times 180.
  2. 2
    180=2×90180 = 2 \times 90; 90=2×4590 = 2 \times 45; 45=3×1545 = 3 \times 15; 15=3×515 = 3 \times 5.
  3. 3
    Collect all prime factors: 2×2×2×3×3×5=23×32×52 \times 2 \times 2 \times 3 \times 3 \times 5 = 2^3 \times 3^2 \times 5.
  4. 4
    Verify: 8×9×5=72×5=3608 \times 9 \times 5 = 72 \times 5 = 360. ✓

Answer

360=23×32×5360 = 2^3 \times 3^2 \times 5
Prime factorization expresses any composite number as a product of prime numbers. The result is unique by the Fundamental Theorem of Arithmetic — no matter what order you factor, the prime factors and their exponents are always the same.

About Prime Factorization

Writing a whole number as a product of prime numbers; every composite number has exactly one such representation (up to order).

Learn more about Prime Factorization →

More Prime Factorization Examples

Example 2 hard

Use prime factorization to find [formula] and [formula].

Example 3 easy

Write the prime factorization of [formula] and use it to find all of its factors.

Example 4 medium

A rectangular garden can be arranged as a whole-number rectangle in exactly [formula] different ways

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