Prime Factorization Calculator Formula
Understand the math behind the prime factorization calculator. Each variable explained with a worked example.
Formulas Used
Div By 2
div_by_2 = mod(n, 2) == 0 ? 1 : 0Div By 3
div_by_3 = mod(n, 3) == 0 ? 1 : 0Div By 5
div_by_5 = mod(n, 5) == 0 ? 1 : 0Div By 7
div_by_7 = mod(n, 7) == 0 ? 1 : 0Sqrt N
sqrt_n = sqrt(n)Is Even
is_even = mod(n, 2) == 0 ? 1 : 0Variables
| Variable | Description | Default |
|---|---|---|
n | Number | 84 |
How It Works
Prime Factorization
What Is It?
Every integer greater than 1 can be written as a product of prime numbers in exactly one way (Fundamental Theorem of Arithmetic).
Method: Trial Division
1. Start with the smallest prime (2) 2. If it divides the number, it is a factor; divide and repeat 3. If not, try the next prime (3, 5, 7, 11, ...) 4. Stop when you reach sqrt(n)
Divisibility Quick Checks
This calculator shows divisibility checks. For full factorization of large numbers, a step-by-step approach is needed.
Worked Example
Check divisibility of 84.
- 0184 / 2 = 42 (divisible by 2)
- 0284 / 3 = 28 (divisible by 3)
- 0384 / 5 = 16.8 (not divisible by 5)
- 0484 / 7 = 12 (divisible by 7)
- 0584 = 2² × 3 × 7
Frequently Asked Questions
What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13...
What is the fundamental theorem of arithmetic?
Every integer greater than 1 is either prime or can be written as a unique product of prime numbers (up to ordering).
Why do we only check up to sqrt(n)?
If n has a factor larger than sqrt(n), it must also have a corresponding factor smaller than sqrt(n). So checking up to sqrt(n) is sufficient.
Learn More
Guide
How to Simplify Radicals - Complete Guide
Learn how to simplify radical expressions step by step. Covers square roots, cube roots, rationalizing denominators, and operations with radicals.
Ready to run the numbers?
Open Prime Factorization Calculator