What Is the GCF of 36 and 60?
The greatest common factor (GCF) of 36 and 60 is 12 - the largest whole number that divides both 36 and 60 without a remainder. Enter the numbers below to see listing factors, prime factorization, and Euclidean algorithm steps. Divide 36 and 60 by 12 to simplify 36/60 to 3/5.
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 36, 60
12
Simplified: 36/60 → 3/5
Show work
Step 1: Factors of 36
[1], [2], [3], [4], [6], 9, [12], 18, 36
Step 2: Factors of 60
[1], [2], [3], [4], 5, [6], 10, [12], 15, 20, 30, 60
Common factors (in every list)
1, 2, 3, 4, 6, 12
Greatest common factor = 12
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 36 and 60 Is 12
The greatest common factor of 36 and 60 is 12 - the largest whole number that divides both values evenly. Common factors shared by 36 and 60 are 1, 2, 3, 4, 6, 12; 12 is the greatest among them.
Listing Factors of 36 and 60
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The numbers that appear in both lists are 1, 2, 3, 4, 6, 12, so the greatest common factor is 12.
Prime Factorization of 36 and 60
36 = 2² × 3². 60 = 2² × 3 × 5. Multiply the shared prime powers (2² × 3) to get GCF = 12.
Simplify 36/60 Using the GCF
Divide numerator and denominator by 12: 36 ÷ 12 = 3 and 60 ÷ 12 = 5. So 36/60 in lowest terms is 3/5.
Common Factors of 36 and 60
| Factor | Divides 36? | Divides 60? |
|---|---|---|
| 1 | Yes | Yes |
| 2 | Yes | Yes |
| 3 | Yes | Yes |
| 4 | Yes | Yes |
| 6 | Yes | Yes |
| 12 (GCF) | Yes | Yes |
Frequently Asked Questions
What is the GCF of 36 and 60?
The GCF of 36 and 60 is 12. It is the largest positive integer that divides both 36 and 60 evenly with no remainder. Common factors shared by both numbers are 1, 2, 3, 4, 6, 12; 12 is the greatest among them.
How do you find the GCF of 36 and 60?
List the factors of 36 and 60, then pick the largest number in both lists - that is 12. 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 36 and 60?
The common factors of 36 and 60 are 1, 2, 3, 4, 6, 12. These are the whole numbers that divide both 36 and 60 without a remainder. The greatest among them is 12, which is the GCF.
How do you simplify 36/60 using the GCF?
Divide the numerator and denominator of 36/60 by their GCF (12). 36 ÷ 12 = 3 and 60 ÷ 12 = 5, so 36/60 simplifies to 3/5 in lowest terms.
Is the GCF of 36 and 60 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 36 and 60: 12. The terms differ by context - GCF in grade-school math, GCD in number theory - but the calculation is identical.