Prime Factorization Calculator

1. Enter a Value: Type any positive integer greater than 1.
2. Click Button: Instantly view prime factor list, exponential representation, and factor tree steps.

According to the Fundamental Theorem of Arithmetic, each integer larger than 1 is either a prime number itself or has a unique factorization into prime numbers, regardless of the order of these factors.

Canonical form: n = p₁^a₁ × p₂^a₂ × ... × pₙ^aₙ, where each $p$ is a prime number.

Example: Factorize 360.

1. 360 ÷ 2 = 180
2. 180 ÷ 2 = 90
3. 90 ÷ 2 = 45
4. 45 ÷ 3 = 15
5. 15 ÷ 3 = 5
6. 5 ÷ 5 = 1
7. Result: 2³ × 3² × 5.

Total Number of Divisors Formula

If $n = p_1^{a} \times p_2^{b} \times p_3^{c}$, the total number of divisors is $(a + 1)(b + 1)(c + 1)$. For 360: $(3+1)(2+1)(1+1) = 4 \times 3 \times 2 = 24$ total divisors.