Factoring Calculator
Find all factors of a number. List divisors and factor pairs for any integer.
Find all factors and factor pairs of any integer. For positive numbers, shows positive factors. For negative numbers, shows all factor pairs including negative factors.
Quick examples:
How to Use
- Enter any positive whole number
- Click "Find Factors" to calculate
- View all factors, factor pairs, and additional information
- Check if the number is prime, composite, or perfect
What is Factoring Calculator?
Factors are numbers that divide evenly into another number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each divides 12 evenly. Finding factors is essential for simplifying fractions, finding GCD/LCM, and understanding number properties.
Formula
A is a factor of N if:
N ÷ A has no remainder (N mod A = 0)
Factor pairs: If A × B = N, then both A and B are factors
Examples
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 7: 1, 7 (prime number)
FAQ
What is the difference between factors and multiples?
Factors divide INTO a number (12's factors include 3), while multiples are what you get when you multiply BY a number (multiples of 3 include 12). Factors are finite; multiples are infinite.
What is a perfect number?
A perfect number equals the sum of its proper divisors (all factors except itself). For example, 6 = 1 + 2 + 3, and 28 = 1 + 2 + 4 + 7 + 14.
How many factors does a number have?
Prime numbers have exactly 2 factors (1 and themselves). Composite numbers have more. Numbers with many factors (like 24, 36, 60) are called highly composite numbers.