What Is the GCF of 8 and 12?
The greatest common factor (GCF) of 8 and 12 is 4 - the largest whole number that divides both 8 and 12 without a remainder. Enter the numbers below to see listing factors, prime factorization, and Euclidean algorithm steps. Divide 8 and 12 by 4 to simplify 8/12 to 2/3.
Enter whole numbers
Type two or more integers separated by commas or spaces.
Result
Greatest common factor (GCF), also called HCF or GCD.
GCF of 8, 12
4
Simplified: 8/12 → 2/3
Show work
Step 1: Factors of 8
[1], [2], [4], 8
Step 2: Factors of 12
[1], [2], 3, [4], 6, 12
Common factors (in every list)
1, 2, 4
Greatest common factor = 4
Methodology and limitations
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Methodology
Computes the greatest common factor using the Euclidean algorithm for the final answer, with optional step-by-step work via listing factors, prime factorization, or repeated division with remainders.
Limitations
Inputs must be whole numbers within JavaScript safe-integer range. GCF(0, 0) is undefined. Step-by-step listing and prime factorization are hidden for very large values to keep the page responsive.
The GCF of 8 and 12 Is 4
The greatest common factor of 8 and 12 is 4 - the largest whole number that divides both values evenly. Common factors shared by 8 and 12 are 1, 2, 4; 4 is the greatest among them.
Listing Factors of 8 and 12
Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. The numbers that appear in both lists are 1, 2, 4, so the greatest common factor is 4.
Prime Factorization of 8 and 12
8 = 2³. 12 = 2² × 3. Multiply the shared prime powers (2²) to get GCF = 4.
Simplify 8/12 Using the GCF
Divide numerator and denominator by 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3. So 8/12 in lowest terms is 2/3.
Common Factors of 8 and 12
| Factor | Divides 8? | Divides 12? |
|---|---|---|
| 1 | Yes | Yes |
| 2 | Yes | Yes |
| 4 (GCF) | Yes | Yes |
Frequently Asked Questions
What is the GCF of 8 and 12?
The GCF of 8 and 12 is 4. It is the largest positive integer that divides both 8 and 12 evenly with no remainder. Common factors shared by both numbers are 1, 2, 4; 4 is the greatest among them.
How do you find the GCF of 8 and 12?
List the factors of 8 and 12, then pick the largest number in both lists - that is 4. You can also use prime factorization: multiply the shared prime powers, or apply the Euclidean algorithm by dividing the larger number by the smaller until the remainder is zero. All three methods are shown in the calculator above.
What are the common factors of 8 and 12?
The common factors of 8 and 12 are 1, 2, 4. These are the whole numbers that divide both 8 and 12 without a remainder. The greatest among them is 4, which is the GCF.
How do you simplify 8/12 using the GCF?
Divide the numerator and denominator of 8/12 by their GCF (4). 8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8/12 simplifies to 2/3 in lowest terms.
Is the GCF of 8 and 12 the same as the GCD?
Yes. GCF (greatest common factor), HCF (highest common factor), and GCD (greatest common divisor) all name the same value for 8 and 12: 4. The terms differ by context - GCF in grade-school math, GCD in number theory - but the calculation is identical.