Number Factorization Calculator
Factors Calculator
Quick Access to Common Factors
Sample Factorizations
Featured Examples
Factors of 24
1, 2, 3, 4, 6, 8, 12, 24
Prime factorization: 23 × 3
Factors of 50
1, 2, 5, 10, 25, 50
Prime factorization: 2 × 52
Factors of 100
1, 2, 4, 5, 10, 20, 25, 50, 100
Prime factorization: 22 × 52
Understanding Factors
Factors are numbers that divide evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides into 12 with no remainder.
Types of Factors
| Type | Description | Example |
|---|---|---|
| Prime Factors | Factors that are prime numbers | 2, 3, 5, 7, 11, etc. |
| Composite Factors | Factors that are not prime numbers | 4, 6, 8, 9, 10, etc. |
| Common Factors | Factors shared between two or more numbers | Factors of 12 and 18: 1, 2, 3, 6 |
Properties of Factors
- Every number is a factor of itself
- 1 is a factor of every number
- The number of factors a number has depends on its prime factorization
- Prime numbers have exactly two factors: 1 and themselves
- Perfect squares have an odd number of factors
Real-World Applications
Understanding factors is crucial in many real-world scenarios:
Architecture
Used in designing tile layouts and determining dimensions for balanced room proportions.
Music Theory
Applied in understanding rhythm patterns and time signatures.
Computer Science
Essential in encryption algorithms and optimization problems.
Prime Factorization Calculator
Find the prime factorization of any number:
Popular Prime Factorizations
Prime Factors of 60
60 = 22 × 3 × 5
Prime factors: 2, 3, 5
Prime Factors of 100
100 = 22 × 52
Prime factors: 2, 5
Prime Factors of 144
144 = 24 × 32
Prime factors: 2, 3
Understanding Prime Factorization
Prime factorization is the process of breaking down a number into a product of prime numbers. A prime number is a number that has exactly two factors: 1 and itself.
What are Prime Factors?
Prime factors are the prime numbers that multiply together to make the original number. For example, the prime factors of 12 are 2 and 3, because 12 = 2 × 2 × 3.
Why are Prime Factors Important?
Prime factorization helps in:
- Finding the Greatest Common Divisor (GCD)
- Calculating the Least Common Multiple (LCM)
- Simplifying fractions
- Understanding number properties