What Is the GCF of 16 and 28?
The greatest common factor (GCF) of 16 and 28 is 4 - the largest whole number that divides both 16 and 28 without a remainder. Enter the numbers below to see listing factors, prime factorization, and Euclidean algorithm steps. Divide 16 and 28 by 4 to simplify 16/28 to 4/7.
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 16, 28
4
Simplified: 16/28 → 4/7
Show work
Step 1: Factors of 16
[1], [2], [4], 8, 16
Step 2: Factors of 28
[1], [2], [4], 7, 14, 28
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 16 and 28 Is 4
The greatest common factor of 16 and 28 is 4 - the largest whole number that divides both values evenly. Common factors shared by 16 and 28 are 1, 2, 4; 4 is the greatest among them.
Listing Factors of 16 and 28
Factors of 16: 1, 2, 4, 8, 16. Factors of 28: 1, 2, 4, 7, 14, 28. The numbers that appear in both lists are 1, 2, 4, so the greatest common factor is 4.
Prime Factorization of 16 and 28
16 = 2⁴. 28 = 2² × 7. Multiply the shared prime powers (2²) to get GCF = 4.
Simplify 16/28 Using the GCF
Divide numerator and denominator by 4: 16 ÷ 4 = 4 and 28 ÷ 4 = 7. So 16/28 in lowest terms is 4/7.
Common Factors of 16 and 28
| Factor | Divides 16? | Divides 28? |
|---|---|---|
| 1 | Yes | Yes |
| 2 | Yes | Yes |
| 4 (GCF) | Yes | Yes |
Frequently Asked Questions
What is the GCF of 16 and 28?
The GCF of 16 and 28 is 4. It is the largest positive integer that divides both 16 and 28 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 16 and 28?
List the factors of 16 and 28, 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 16 and 28?
The common factors of 16 and 28 are 1, 2, 4. These are the whole numbers that divide both 16 and 28 without a remainder. The greatest among them is 4, which is the GCF.
How do you simplify 16/28 using the GCF?
Divide the numerator and denominator of 16/28 by their GCF (4). 16 ÷ 4 = 4 and 28 ÷ 4 = 7, so 16/28 simplifies to 4/7 in lowest terms.
Is the GCF of 16 and 28 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 16 and 28: 4. The terms differ by context - GCF in grade-school math, GCD in number theory - but the calculation is identical.