Factor Calculator
Find factors, prime factorization, GCD, and LCM
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📚 Examples, Rules & Help
⚡Quick Examples - Try These Calculations
🔍How It Works
Finding Factors
Method: Test divisibility from 1 to √n
For each divisor i found, both i and n/i are factors.
Example for 24:
√24 ≈ 4.9, so test 1, 2, 3, 4
• 1 divides 24 → factors: 1, 24
• 2 divides 24 → factors: 2, 12
• 3 divides 24 → factors: 3, 8
• 4 divides 24 → factors: 4, 6
Prime Factorization
Method: Divide by smallest primes repeatedly
Example for 60:
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
GCD & LCM
GCD: Largest number that divides both numbers
LCM: Smallest number that both numbers divide
Relationship:
GCD(a,b) × LCM(a,b) = a × b
Example: GCD(12,18) = 6, LCM(12,18) = 36
Check: 6 × 36 = 216 = 12 × 18 ✓
🌍Real-World Applications
❓Frequently Asked Questions
What's the difference between factors and multiples?
Factors divide into the number evenly. For 12: factors are 1, 2, 3, 4, 6, 12
Multiples are the number multiplied by integers. For 12: multiples are 12, 24, 36, 48...
Think: factors go INTO the number, multiples come FROM the number.
Why is prime factorization useful?
Prime factorization is the "DNA" of a number - it uniquely identifies the number.
Uses:
• Finding GCD and LCM efficiently
• Simplifying fractions and radicals
• Understanding number properties
• Cryptography and computer science
How do I find GCD and LCM quickly?
Using prime factorization:
• GCD: Take lowest power of each common prime
• LCM: Take highest power of each prime that appears
Example: 12 = 2² × 3, 18 = 2 × 3²
GCD = 2¹ × 3¹ = 6
LCM = 2² × 3² = 36
Can negative numbers have factors?
Yes! Negative numbers have the same positive factors as their absolute value, plus all the negative versions.
Example: Factors of -12 include both ±1, ±2, ±3, ±4, ±6, ±12
For simplicity, we usually focus on positive factors and note that negatives also work.
🎯Common Use Cases
🎓 Educational Use
- • Understanding prime and composite numbers
- • Practicing multiplication and division
- • Learning about mathematical relationships
- • Homework and test preparation
🧮 Practical Math
- • Simplifying fractions in recipes
- • Finding common denominators
- • Calculating gear ratios
- • Scheduling and time management
💻 Programming
- • Algorithm optimization
- • Hash function design
- • Cryptographic calculations
- • Mathematical modeling
🔬 Advanced Math
- • Number theory research
- • Abstract algebra
- • Discrete mathematics
- • Mathematical proofs