Calculadora de Factores
Encuentra factores, MCD, MCM y factorización prima
Free Math Calculators & Tools
10 specialized calculators for factors, primes, GCF, LCM, divisibility, multiples, and number properties — each with interactive visualizations and step-by-step explanations.
What are Factors?
Factors are whole numbers that divide evenly into another number with zero remainder. Every positive integer has at least 2 factors: 1 and the number itself. A factor calculator finds all these divisors instantly.
The number 12, for example, has 6 factors: 1, 2, 3, 4, 6, and 12. Each factor divides 12 without leaving a remainder. Prime numbers like 2, 3, 5, and 7 have exactly 2 factors. Composite numbers like 12, 18, and 24 have 3 or more factors.
Factors connect directly to the multiplication table. The factor pair (3, 4) means 3 × 4 = 12. Finding all factor pairs of a number is the same as finding every way to express the number as a product of 2 whole numbers. This concept is foundational in number theory and appears in prime factorization, Greatest Common Factor (GCF) calculation, and Least Common Multiple (LCM) computation.
Interactive Factor Rainbow
Pick a number to see its factor pairs connected by arcs.
How to Find Factors
To find all factors of a number, divide the number by every integer from 1 up to its square root. Each division with zero remainder reveals a factor pair. This trial division method is the most direct approach and the same method used by a factor calculator.
There are 3 standard methods to find factors of any positive integer:
- Trial Division — Divide by each integer from 1 to √n. Each zero-remainder division gives 2 factors: the divisor and the quotient.
- Factor Tree — Break a composite number into 2 factors, then break each factor further until all branches end in prime numbers. The result is the prime factorization.
- Divisibility Rules — Use shortcut rules (even → divisible by 2, digit sum divisible by 3 → divisible by 3, ends in 0 or 5 → divisible by 5) to quickly test common divisors.
The trial division method works for all numbers up to 10,000,000 in this factor calculator. The Sieve of Eratosthenes generates prime numbers efficiently, and the Euclidean algorithm finds the Greatest Common Factor (GCF) between 2 numbers using repeated division.
Trial Division Walkthrough
Pick a number to watch the division method find all its factors.
Method: Divide 36 by each integer from 1 to √36 ≈ 6. Zero remainder = factor found.
All 9 factors of 36:
Examples
The factor calculator with steps below shows 4 worked examples: 36, 48, 100, and 60. Each example lists all factors, factor pairs, and the prime factorization. Click any card to expand the full breakdown.
Factors of 36
9 factors · 2² × 3²
36 is a perfect square (6 × 6 = 36). The number 36 has 9 factors and 5 factor pairs. The prime factorization of 36 breaks down into 2 squared times 3 squared. The factor count formula gives (2+1)(2+1) = 9 factors.
All Factors
Factor Pairs
Prime Factorization
2² × 3²
Sum of Factors
91
Factors of 48
10 factors · 2⁴ × 3
Factors of 100
9 factors · 2² × 5²
Factors of 60
12 factors · 2² × 3 × 5
Dynamic Factor Pair Visualization
Factor pairs are 2 integers whose product equals the original number. The number 36, for example, has 5 factor pairs: (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). A factor pair where both numbers are equal indicates a perfect square. Integer factorization and prime factor decomposition are central operations in number theory and form the basis of modern cryptography key generation.
The factor tree breaks a composite number down into prime numbers through repeated division. Each branch splits into 2 factors until all leaf nodes are prime. This process gives the complete prime factorization used in GCF and LCM calculations.
Frequently Asked Questions
Answers to 8 common questions about factors, prime factorization, GCF, LCM, and factor pairs.