Factor Calculator
Find all factors of any positive integer. Enter a number to see its complete list of factors, factor pairs, prime factorization, and detailed mathematical analysis.
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Quick Examples:
Methods to Find Factors
1. Division Method
Test each number from 1 to the square root of the given number. If it divides evenly, both the divisor and quotient are factors.
2. Prime Factorization Method
Find the prime factorization, then generate all possible combinations of prime factors.
3. Factor Tree Method
Break down the number into smaller factors repeatedly until only prime factors remain.
How to Use This Calculator
Understanding Factors
What are Factors?
A factor of a number is any integer that divides the number evenly (with no remainder). For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 without leaving a remainder.
Types of Factors
Proper Divisors
All factors of a number except the number itself. For 12: 1, 2, 3, 4, 6.
Prime Factors
Factors that are prime numbers. For 12: 2 and 3.
Composite Factors
Factors that are composite numbers. For 12: 4, 6, and 12.
Factor Pairs
Two factors that multiply to give the original number. For 12: (1,12), (2,6), (3,4).
Special Numbers
Prime Numbers
Numbers with exactly two factors: 1 and themselves. Examples: 2, 3, 5, 7, 11.
Perfect Numbers
Numbers equal to the sum of their proper divisors. Example: 6 = 1 + 2 + 3.
Perfect Squares
Numbers with an odd number of factors. Examples: 1, 4, 9, 16, 25.
Highly Composite
Numbers with more factors than any smaller positive integer. Examples: 1, 2, 4, 6, 12.
Example Calculations
Example 1: Small Number (12)
Example 2: Perfect Square (36)
Example 3: Prime Number (17)
Frequently Asked Questions
What's the difference between factors and multiples?
Factors divide into a number evenly, while multiples are the result of multiplying a number by integers. For example, factors of 12 are 1, 2, 3, 4, 6, 12, while multiples of 12 are 12, 24, 36, 48, etc.
Why do perfect squares have an odd number of factors?
Most factors come in pairs that multiply to give the original number. However, perfect squares have one factor (the square root) that pairs with itself, resulting in an odd total count.
How can I quickly check if a number is prime?
A number is prime if it has exactly two factors: 1 and itself. You only need to test divisibility up to the square root of the number. If no factors are found in that range, the number is prime.