Factor Calculator Find all factors, prime factors, GCF, LCM, and factor pairs of any number — with step-by-step explanati...
Factor Calculator
Find all factors, prime factors, GCF, LCM, and factor pairs of any number — with step-by-step explanations.
All Factors
Prime Factorization
GCF & LCM
Factor Pairs
24
Original Number
8
Total Factors
2
Prime Factors
All Factors
Calculation Type
1
2
3
4
6
8
12
24
Factor Formulas
All Factors
Find all divisors
Prime Factors
n = p₁^a₁ × p₂^a₂ × ...
GCF
Greatest Common Factor
LCM
Least Common Multiple
Interpretation
—
Factor Visualization
Factor Fundamentals
A factor of a number is an integer that divides evenly into that number with no remainder.
Key Concepts**:
- Factors**: Numbers that divide evenly into another number
- Prime Factors**: Prime numbers that multiply together to give the original number
- GCF**: Greatest Common Factor - largest number that divides two numbers
- LCM**: Least Common Multiple - smallest number divisible by two numbers
- Factor Pairs**: Two numbers that multiply to give the original number
Why It Matters**:
- Essential for simplifying fractions
- Used in finding common denominators
- Important in algebra for factoring polynomials
- Fundamental in number theory and cryptography
✅ Example**: Factors of 12 are 1, 2, 3, 4, 6, 12. Prime factors are 2² × 3.
Common Factor Calculation Mistakes
⚠️ Avoid these frequent errors:
- Missing factors**: Forgetting 1 and the number itself
- Prime factorization errors**: Not breaking down completely to primes
- GCF vs LCM confusion**: Mixing up greatest common factor with least common multiple
- Negative numbers**: Factors are typically positive integers
- Zero handling**: Zero has infinitely many factors, but GCF/LCM with zero is undefined
✅ Best Practices**:
- Always start with 1 and the number itself
- Check divisibility rules to find factors quickly
- For prime factorization, divide by smallest primes first
- Use prime factorization method for GCF and LCM of large numbers
Real-World Applications
Factor calculations are essential in:
- Mathematics**: Simplifying fractions, solving equations, number theory
- Computer Science**: Cryptography (RSA encryption), algorithms, data structures
- Engineering**: Gear ratios, signal processing, control systems
- Finance**: Interest calculations, investment periods, risk analysis
- Everyday Life**: Dividing items evenly, recipe scaling, time management
📊 Example Use Cases**:
- Fraction Simplification**: 24/36 = (24÷12)/(36÷12) = 2/3 (GCF=12)
- Event Planning**: 24 guests, tables of 6 → 4 tables needed
- Cryptography**: RSA encryption relies on difficulty of factoring large numbers
- Gear Design**: Gear ratio of 24:36 simplifies to 2:3
How to Use This Calculator
➡️ All Factors
"Find factors of 24" → 1, 2, 3, 4, 6, 8, 12, 24
➡️ Prime Factorization
"Prime factors of 60" → 2² × 3 × 5
➡️ GCF & LCM
"GCF and LCM of 24 and 36" → GCF=12, LCM=72
➡️ Factor Pairs
"Factor pairs of 12" → (1,12), (2,6), (3,4)
Note: All calculations handle positive integers. For GCF/LCM, the calculator uses the prime factorization method for accuracy.