What Is the GCF of 30 and 54?
The greatest common factor (GCF) of 30 and 54 is 6 - the largest whole number that divides both 30 and 54 without a remainder. Enter the numbers below to see listing factors, prime factorization, and Euclidean algorithm steps. Divide 30 and 54 by 6 to simplify 30/54 to 5/9.
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 30, 54
6
Simplified: 30/54 → 5/9
Show work
Step 1: Factors of 30
[1], [2], [3], 5, [6], 10, 15, 30
Step 2: Factors of 54
[1], [2], [3], [6], 9, 18, 27, 54
Common factors (in every list)
1, 2, 3, 6
Greatest common factor = 6
Methodology and limitations
Last reviewed:
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 30 and 54 Is 6
The greatest common factor of 30 and 54 is 6 - the largest whole number that divides both values evenly. Common factors shared by 30 and 54 are 1, 2, 3, 6; 6 is the greatest among them.
Listing Factors of 30 and 54
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. The numbers that appear in both lists are 1, 2, 3, 6, so the greatest common factor is 6.
Prime Factorization of 30 and 54
30 = 2 × 3 × 5. 54 = 2 × 3³. Multiply the shared prime powers (2 × 3) to get GCF = 6.
Simplify 30/54 Using the GCF
Divide numerator and denominator by 6: 30 ÷ 6 = 5 and 54 ÷ 6 = 9. So 30/54 in lowest terms is 5/9.
Common Factors of 30 and 54
| Factor | Divides 30? | Divides 54? |
|---|---|---|
| 1 | Yes | Yes |
| 2 | Yes | Yes |
| 3 | Yes | Yes |
| 6 (GCF) | Yes | Yes |
Frequently Asked Questions
What is the GCF of 30 and 54?
The GCF of 30 and 54 is 6. It is the largest positive integer that divides both 30 and 54 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 30 and 54?
List the factors of 30 and 54, 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 30 and 54?
The common factors of 30 and 54 are 1, 2, 3, 6. These are the whole numbers that divide both 30 and 54 without a remainder. The greatest among them is 6, which is the GCF.
How do you simplify 30/54 using the GCF?
Divide the numerator and denominator of 30/54 by their GCF (6). 30 ÷ 6 = 5 and 54 ÷ 6 = 9, so 30/54 simplifies to 5/9 in lowest terms.
Is the GCF of 30 and 54 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 30 and 54: 6. The terms differ by context - GCF in grade-school math, GCD in number theory - but the calculation is identical.