🔢 Factor Calculator
Find all factors (divisors), factor pairs & prime factorization instantly.
What is a Factor?
A factor (or divisor) of a number is an integer that divides that number exactly without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because 12 ÷ 1 = 12, 12 ÷ 2 = 6, etc.
Factor Pairs
Factors often come in pairs that multiply together to give the original number. The factor pairs of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). This tool lists all factor pairs for any number you enter.
Prime Factorization
Prime factorization expresses a number as the product of its prime factors. For instance, 36 = 2² × 3². Understanding prime factors is essential for simplifying fractions, finding greatest common divisors (GCD), and least common multiples (LCM).
How to Use the Factor Calculator
- Type any positive integer (whole number greater than 0) into the input box.
- Press Calculate or use one of the quick‑select buttons (36, 48, 100, 120, 256).
- The tool instantly displays all factors, factor pairs, and the prime factorization with exponents.
Why Use This Calculator?
- ✅ Instant results – No page reload or server call; everything runs in your browser.
- ✅ Easy to understand – Clean, beginner‑friendly layout.
- ✅ Educational – Shows factor pairs and prime factorization to help you learn.
- ✅ Mobile responsive – Works perfectly on phones and tablets.
Common Factor Examples
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 → Prime factorization: 2³ × 3
- Factors of 50: 1, 2, 5, 10, 25, 50 → Prime factorization: 2 × 5²
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 → Prime factorization: 2³ × 3²
Try the calculator above to explore any number you like!
