What Is the GCF of 18 and 24?
The greatest common factor (GCF) of 18 and 24 is 6 - the largest whole number that divides both 18 and 24 without a remainder. Enter the numbers below to see listing factors, prime factorization, and Euclidean algorithm steps. Divide 18 and 24 by 6 to simplify 18/24 to 3/4.
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 18, 24
6
Simplified: 18/24 → 3/4
Show work
Step 1: Factors of 18
[1], [2], [3], [6], 9, 18
Step 2: Factors of 24
[1], [2], [3], 4, [6], 8, 12, 24
Common factors (in every list)
1, 2, 3, 6
Greatest common factor = 6
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 18 and 24 Is 6
The greatest common factor of 18 and 24 is 6 - the largest whole number that divides both values evenly. Common factors shared by 18 and 24 are 1, 2, 3, 6; 6 is the greatest among them.
Listing Factors of 18 and 24
Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The numbers that appear in both lists are 1, 2, 3, 6, so the greatest common factor is 6.
Prime Factorization of 18 and 24
18 = 2 × 3². 24 = 2³ × 3. Multiply the shared prime powers (2 × 3) to get GCF = 6.
Simplify 18/24 Using the GCF
Divide numerator and denominator by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. So 18/24 in lowest terms is 3/4.
Common Factors of 18 and 24
| Factor | Divides 18? | Divides 24? |
|---|---|---|
| 1 | Yes | Yes |
| 2 | Yes | Yes |
| 3 | Yes | Yes |
| 6 (GCF) | Yes | Yes |
Frequently Asked Questions
What is the GCF of 18 and 24?
The GCF of 18 and 24 is 6. It is the largest positive integer that divides both 18 and 24 evenly with no remainder. Common factors shared by both numbers are 1, 2, 3, 6; 6 is the greatest among them.
How do you find the GCF of 18 and 24?
List the factors of 18 and 24, then pick the largest number in both lists - that is 6. 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 18 and 24?
The common factors of 18 and 24 are 1, 2, 3, 6. These are the whole numbers that divide both 18 and 24 without a remainder. The greatest among them is 6, which is the GCF.
How do you simplify 18/24 using the GCF?
Divide the numerator and denominator of 18/24 by their GCF (6). 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18/24 simplifies to 3/4 in lowest terms.
Is the GCF of 18 and 24 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 18 and 24: 6. The terms differ by context - GCF in grade-school math, GCD in number theory - but the calculation is identical.