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Factor Calculator
Find factors, prime factorization, GCF, and LCM with steps.
Quick answer
How do you find the factors of a number?
Divide the number by every whole number from 1 up to its square root; each one that divides evenly gives a factor pair. The factors of 12 are 1, 2, 3, 4, 6, and 12 (pairs 1×12, 2×6, 3×4). The prime factorization of 72 is 2³ × 3².
Factors divide a number with no remainder. GCF = product of shared primes at their lowest power. LCM = product of all primes at their highest power. For two numbers, GCF × LCM = a × b.
⚡ Answer updates as you type · Enter = calculate · Esc = reset
- Test every whole number from 1 up to √72 ≈ 8.4853.
- Factor pairs: 1 × 72, 2 × 36, 3 × 24, 4 × 18, 6 × 12, 8 × 9.
- Divide by primes repeatedly: 72 = 2 × 2 × 2 × 3 × 3 = 2^3 × 3^2.
- Sum of factors: 195.
List all factors and factor pairs, find the prime factorization, and get the greatest common factor and least common multiple — with steps.
About this Factor Calculator
The Factor Calculator lists every factor and factor pair of a number, shows its prime factorization in exponent form, and tells you whether it is prime or composite. Switch modes to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers using prime factor steps.
What you'll need
- • Mode: factors & prime factorization, or GCF & LCM
- • A whole number
- • Two or more whole numbers separated by commas
How it works
- 1. Choose factors or GCF & LCM.
- 2. Enter your number or list of numbers.
- 3. The calculator tests divisors up to the square root.
- 4. It breaks each number into primes.
- 5. Read the factors, GCF, LCM, and every step.
Worked example
12 = 2² × 3 and 18 = 2 × 3². Shared primes at lowest power: 2 × 3 = 6, so GCF = 6. All primes at highest power: 2² × 3² = 36, so LCM = 36.
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Factor Calculator FAQ
What is the Factor Calculator?
The Factor Calculator is a free online tool that helps you find factors, prime factorization, gcf, and lcm with steps.
How do I use the Factor Calculator?
Open the Factor Calculator, enter the requested values, and review the instant estimate on the page.
Is the Factor Calculator free?
Yes. The Factor Calculator is free to use on Fast Online Calculator and does not require an account.
What are the factors of 24?
1, 2, 3, 4, 6, 8, 12, and 24. The factor pairs are 1×24, 2×12, 3×8, and 4×6.
What is the difference between GCF and LCM?
The GCF is the largest number that divides all your numbers. The LCM is the smallest number all your numbers divide into. For 4 and 6, GCF = 2 and LCM = 12.
Is 1 a prime number?
No. A prime has exactly two factors, 1 and itself. 1 has only one factor, so it is neither prime nor composite.
When do I use GCF vs LCM?
Use the GCF to simplify fractions or split things into equal groups. Use the LCM to find a common denominator or when repeating events line up.
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