GCF vs the full common-factor list
Homework that says “find the GCF” needs the single top number (6 for 12, 18, 24). Problems that say “list all common factors” need the whole ascending list. Both show in the dark results panel.
Modular arithmetic & digits
Common Factor Calculator
GCF plus every shared divisor for two or more integers, with prime breakdowns.
By Jeff Beem
Updated
Numbers
Positive integers only (1 or more numbers). Non-numeric characters are ignored. No limit on how many numbers, enter as many as you need.
Result
Greatest Common Factor (GCF)6
All common factors (4)
1, 2, 3, 6
Individual factor breakdown
| Number | Divisors |
|---|---|
| 12 | 1, 2, 3, 4, 6, 12 |
| 18 | 1, 2, 3, 6, 9, 18 |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 |
How it was calculated
Prime factorization for each number. The GCF is the product of the lowest power of all common prime bases.
- 12=2^2 × 3
- 18=2 × 3^2
- 24=2^3 × 3
Using this calculator
The greatest common factor is the largest shared divisor; the line below lists every common factor (default 12, 18, 24 → GCF 6, factors 1, 2, 3, 6). The table shows all divisors per number; “How it was calculated” shows prime factorization steps.
Example: 12, 18, 24 → GCF 6
With 12, 18, and 24 in the box, the GCF is 6 and the shared divisors are 1, 2, 3, 6. Twelve splits into 1, 2, 3, 4, 6, 12; eighteen adds 9 and 18; twenty-four adds 8 and 24. Only 1, 2, 3, and 6 appear in all three lists.
What to read in the results
Factor table for side-by-side divisors
Each input number gets its own divisor row so you can spot overlap without doing three lists on paper. Handy when a teacher wants to see that 6 divides 12, 18, and 24.
Prime lines under “How it was calculated”
12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. Shared primes at the lowest exponent give 2 × 3 = 6. That section is for showing work, not just the final GCF.
Copy when the list is the answer
“Copy common factors” pastes 1, 2, 3, 6 (for the default triple) into a worksheet or doc. Non-numeric characters in the input are ignored; results update as you type.
Common factor calculator: GCF and every shared divisor
12, 18, 24 → GCF 6 and common factors 1, 2, 3, 6. Euclidean steps, divisor lists, and prime breakdowns for two or more integers.
What this calculator does
Accepts a comma-separated list of positive integers and returns the greatest common factor (GCF), every common factor in ascending order, a per-number divisor table, and prime factorizations in “How it was calculated.” Uses the Euclidean algorithm for the GCF and set intersection for the full common-factor list. Ignores non-numeric input; does not handle decimals, negatives, or fractions inside the list.
- Outputs:GCF, full common-factor list, divisor table, prime lines.
- Limits:Positive integers only; very large values are capped at safe integer range in the browser.
How the math works
For two numbers, repeat GCF(a, b) = GCF(b, a mod b) until the remainder is 0. GCF(24, 36): 36 mod 24 = 12, then 24 mod 12 = 0, so the GCF is 12. For three numbers, fold left to right: GCF(12, 18, 24) = GCF(GCF(12, 18), 24) = GCF(6, 24) = 6. The full common-factor list builds by listing all divisors of each input and keeping numbers that appear in every list. Prime method: 12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3; take the lowest power of each shared prime → 2 × 3 = 6.
- Euclidean:Remainders until zero; last non-zero remainder is the GCF for that pair.
- All common factors:Intersection of divisor sets, sorted ascending.
- Primes:Lowest exponent on each shared base; multiply for the GCF.
Using the form
The box opens with 12, 18, 24. Change it to any list (two numbers like 12, 18 or longer runs like 24, 36, 60). GCF sits at the top of the results panel; common factors sit just below with a copy button. Expand “How it was calculated” when you need prime strings for each entry.
Factor vs multiple
A factor divides the number evenly (1, 2, 3, 6 for 12). A multiple is what you get multiplying by 1, 2, 3, … (12, 24, 36, … for 12). Common factors are divisors every number in your list shares; the GCF is the largest of those.
GCF and GCD
GCF and GCD name the same integer. Textbooks and search queries swap the words; the math does not. This page prints both labels in places students recognize, but the computed value is one number.
By hand: list and intersect
Write divisors for each number (stop at √n and pair factors to save steps). Cross out anything not in every list. The biggest survivor is the GCF. For 12 and 18 alone, shared divisors are 1, 2, 3, 6; GCF is 6. For three or more numbers, intersect all lists before picking the maximum.
Common Factor Calculator FAQ
What is the common factor of 12 and 18?
The numbers that divide both evenly are 1, 2, 3, and 6. The largest is the GCF: 6. List divisors of each number and keep the overlap, or type 12, 18 here and read the GCF plus the full common-factor list.
Can a common factor be a decimal?
No. Factors are whole-number divisors with zero remainder. This tool only accepts positive integers. For ratios or fractions, simplify with a fraction or ratio calculator instead.
Is 1 always a common factor?
Yes. One divides every positive integer, so any list of two or more whole numbers always shares 1. If 1 is the only overlap, the numbers are coprime (relatively prime). The GCF is still at least 1.
What is the difference between GCF and GCD?
Same value, different names: GCF (greatest common factor) and GCD (greatest common divisor) both mean the largest integer that divides every number in your list with no remainder.
How do I find the greatest common factor of 3 numbers?
Chain the pairwise GCF: GCF(12, 18, 24) = GCF(6, 24) = 6. You can also list divisors of each number and intersect the lists. Enter 12, 18, 24 (or any comma-separated list) to see the GCF, every common factor, and prime breakdowns.
Mathematical Reference Note
Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.
Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.
Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.
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