Factor Calculator
Deconstruct any integer into its fundamental building blocks.
Factor Calculator
This calculator finds all factors of any integer and its complete prime factorization — showing every number that divides evenly into your input, organized into factor pairs.
How to Use This Calculator
- Enter any positive integer.
- Click Calculate to see: all factors listed, factor pairs, and complete prime factorization.
What Are Factors?
A factor of n is any integer that divides n without a remainder. Every number has at least two factors: 1 and itself. A prime number has exactly two factors; composite numbers have more.
Example: Factors of 60
60 = 2² × 3 × 5 (prime factorization)
Factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factor pairs: (1,60), (2,30), (3,20), (4,15), (5,12), (6,10)
How to Find Prime Factorization
- Divide by the smallest prime (2) as many times as possible.
- Move to the next prime (3, 5, 7...) and repeat.
- Stop when the quotient is 1.
360: 360÷2=180÷2=90÷2=45÷3=15÷3=5÷5=1 → 2³ × 3² × 5
Common Mistakes to Avoid
- Forgetting 1 and the number itself as factors — Every integer ≥ 1 has at least these two factors.
- Confusing prime factors with all factors — Prime factors are 2, 3, 5 for 60. All factors include 1, 4, 6, 10, 12, 15, 20, 30, 60 as well.
- Thinking 1 is prime — 1 is neither prime nor composite. Prime numbers have exactly two factors; 1 has only one.
Frequently Asked Questions
How many factors does a prime number have?
Exactly two: 1 and itself. That's the definition of a prime number. 17 has factors 1 and 17 only.
What is a perfect number?
A number equal to the sum of its proper factors (excluding itself). 6 = 1+2+3. 28 = 1+2+4+7+14. Only five perfect numbers are known up to very large values.
How do I use factoring to simplify fractions?
Find GCF of numerator and denominator using their factors, then divide both by the GCF. See our GCF Calculator.
Conclusion
Understanding factors is fundamental to number theory, fraction work, and algebra. Use this calculator to instantly find every factor and the prime factorization of any number — with organized factor pairs for clarity.
Related: GCF Calculator | LCM Calculator | Fraction Calculator
Expert Advice
Use the factor pair table to find the dimensions of shapes. If you have 60 square feet, the table shows all possible rectangular dimensions with whole numbers.
