Enter any positive integer to instantly list all its factors, factor pairs, prime factorization (with exponents), total factor count, sum of factors, and primality status.
How to use this calculator
Enter a positive integer n.
Read all factors listed in ascending order and grouped as factor pairs.
The prime factorization is shown with exponent notation (e.g. 120 = 2³ × 3 × 5).
Formula & method
Trial division for factors and prime factorization
Factors: check every integer 1 to √n · Prime factorization: divide by smallest prime repeatedly
Factor pairs: for each factor a ≤ √n, pair it with n/a. Number of factors σ₀(n) counts the total divisors.
Example
n = 120: factors 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 (16 factors). Prime factorization: 2³ × 3 × 5.
Key insights
A prime number has exactly 2 factors: 1 and itself (e.g. 7, 13, 97).
A perfect number equals the sum of its proper divisors: 6 = 1 + 2 + 3.
The number of factors is a key concept in divisibility rules and number theory.
Every integer n > 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).
How to interpret your result
Factor pairs
Factor pairs (a, b) are pairs where a × b = n. They come in pairs around √n; if n is a perfect square, one pair has a = b.
Prime factorization
Writing n as a product of primes with exponents: 120 = 2³ × 3 × 5. Used to compute GCF and LCM efficiently.
Frequently asked questions
What are factors of a number?
Factors (divisors) of n are all positive integers that divide n without a remainder. 120 has 16 factors.
What is prime factorization?
Writing a number as a product of primes. By the Fundamental Theorem of Arithmetic, every integer > 1 has a unique prime factorization.
How is this different from the GCF Calculator?
The Factor Calculator lists all factors of a single number. The GCF Calculator finds the greatest common factor of two or more numbers.
Related calculators
GCF Calculator — Find the Greatest Common Factor (GCF/GCD) and all common factors of two or more integers using the Euclidean algorithm.
LCM Calculator — Find the Least Common Multiple (LCM) of two or more integers to solve fraction addition and scheduling problems.
Long Division Calculator — Perform integer long division with remainder, mixed number result, and step-by-step verification.