Factor Calculator
Find all factors, prime factorization, factor pairs, number of factors, and sum of factors for any positive integer.
Prime Factorization
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Number of Factors
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Sum of Factors
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All Factors
Factor Pairs
What is Factor Calculator?
The factor calculator finds all divisors of a positive integer using trial division. It displays all factors, factor pairs, complete prime factorization with exponents, the total number of factors, and the sum of all factors.
How to use
- 1 Enter any positive integer in the input field.
- 2 Click Calculate to see the complete factor analysis.
- 3 Review all factors listed in order.
- 4 See prime factorization expressed with exponents (e.g., 2³ × 3).
- 5 Factor pairs show every combination of two numbers that multiply to the original.
Formula
Example calculation
n = 360: Factors: 1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360. Prime factorization: 2³ × 3² × 5. Number of factors: (3+1)(2+1)(1+1) = 24. Sum = 1170.
Frequently asked questions
What is a factor?
A factor (or divisor) of a number n is any integer that divides n evenly with no remainder. For example, factors of 12 are 1, 2, 3, 4, 6, and 12.
What is prime factorization?
Prime factorization expresses a number as a product of prime numbers. Every integer greater than 1 has a unique prime factorization (the Fundamental Theorem of Arithmetic).
What is a prime number?
A prime number has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13. The number 1 is not considered prime.
What are factor pairs?
Factor pairs are sets of two numbers that multiply together to give the original number. For 12: (1,12), (2,6), (3,4).
What is the sum of factors used for?
The sum of proper factors (excluding the number itself) determines if a number is perfect (sum = n), abundant (sum > n), or deficient (sum < n). For example, 6 is perfect: 1+2+3 = 6.