Factor Calculator
Find Factors, GCF, LCM & Prime Factorization
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.
- Divisibility Rules — Use shortcut rules (even → divisible by 2, digit sum divisible by 3 → divisible by 3) to test common divisors.
The trial division method works for all numbers up to 10,000,000 in this factor calculator.
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 of Factor Calculator
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.
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. A factor pair where both numbers are equal indicates a perfect square.
The factor tree breaks a composite number down into prime numbers through repeated division.
Free Math Calculators & Tools
10 specialized calculators for factors, primes, GCF, LCM, divisibility, multiples, and number properties.
Frequently Asked Questions
Answers to common questions about factors, prime factorization, GCF, LCM, and factor pairs.