GCF of 3 and 12


The gcf of 3 and 12 is the largest positive integer that divides the numbers 3 and 12 without a remainder. Spelled out, it is the greatest common factor of 3 and 12. Here you can find the gcf of 3 and 12, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the gcf of 3 and 12, but also that of three or more integers including three and twelve for example. Keep reading to learn everything about the gcf (3,12) and the terms related to it.

What is the GCF of 3 and 12

If you just want to know what is the greatest common factor of 3 and 12, it is 3. Usually, this is written as

gcf(3,12) = 3

The gcf of 3 and 12 can be obtained like this:

  • The factors of 3 are 3, 1.
  • The factors of 12 are 12, 6, 4, 3, 2, 1.
  • The common factors of 3 and 12 are 3, 1, intersecting the two sets above.
  • In the intersection factors of 3 ∩ factors of 12 the greatest element is 3.
  • Therefore, the greatest common factor of 3 and 12 is 3.

Taking the above into account you also know how to find all the common factors of 3 and 12, not just the greatest. In the next section we show you how to calculate the gcf of three and twelve by means of two more methods.

How to find the GCF of 3 and 12

The greatest common factor of 3 and 12 can be computed by using the least common multiple aka lcm of 3 and 12. This is the easiest approach:

gcf (3,12) = $\frac{3 \times 12}{lcm(3,12)} = \frac{36}{12}$ = 3

Alternatively, the gcf of 3 and 12 can be found using the prime factorization of 3 and 12:

  • The prime factorization of 3 is: 3
  • The prime factorization of 12 is: 2 x 2 x 3
  • The prime factors and multiplicities 3 and 12 have in common are: 3
  • 3 is the gcf of 3 and 12
  • gcf(3,12) = 3

In any case, the easiest way to compute the gcf of two numbers like 3 and 12 is by using our calculator below. Note that it can also compute the gcf of more than two numbers, separated by a comma. For example, enter 3,12. The calculation is conducted automatically.

The gcf is...
Frequently searched terms on our site also include:

Use of GCF of 3 and 12

What is the greatest common factor of 3 and 12 used for? Answer: It is helpful for reducing fractions like 3 / 12. Just divide the nominator as well as the denominator by the gcf (3,12) to reduce the fraction to lowest terms.

$\frac{3}{12} = \frac{\frac{3}{3}}{\frac{12}{3}} = \frac{1}{4}$.

Properties of GCF of 3 and 12

The most important properties of the gcf(3,12) are:

  • Commutative property: gcf(3,12) = gcf(12,3)
  • Associative property: gcf(3,12,n) = gcf(gcf(12,3),n) $\hspace{10px}n\hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

The associativity is particularly useful to get the gcf of three or more numbers; our calculator makes use of it.

To sum up, the gcf of 3 and 12 is 3. In common notation: gcf (3,12) = 3.

If you have been searching for gcf 3 and 12 or gcf 3 12 then you have come to the correct page, too. The same is the true if you typed gcf for 3 and 12 in your favorite search engine.

Note that you can find the greatest common factor of many integer pairs including three / twelve by using the search form in the sidebar of this page.

Questions and comments related to the gcf of 3 and 12 are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the greatest common factor of 3 and 12 has been useful to you, and make sure to bookmark our site.

Thanks for your visit.

Print Friendly, PDF & Email
Posted in Greatest Common Factor

Leave a Reply

Your email address will not be published. Required fields are marked *

*


Related pages


prime factors of 231is 253 a prime numberwhat is the greatest common factor of 24 and 72prime factorization 54multiplication chart 1-30prime factorization of 92greatest common factor of 42 and 72the prime factorization of 121what is the gcf of 96 and 84what is the prime factorization for 923x times tablesgreatest prime factor of 38is 567 a prime numberwhat is the greatest common factor of 63the prime factorization of 126prime factorization of 196lcm of 5 7prime factors of 252what is the prime factorization of 95prime factors of 720multiplication tables to 100prime factorization 98prime factorization of 232what is the lcm of 30the prime factorization of 175common multiples of 3 and 6greatest common factor of 54 and 36whats the prime factorization of 81is 141 a prime numberwhat is the prime factorization of 39is 847 a prime numberwhat is the prime factorization of 828greatest common factor of 75 and 90highest common factor finderwhat is the prime factorization of 625what is the greatest common factor of 17 and 34prime factorization of 208what is the gcf of 56 and 96prime numbers 1-60express 180 as a product of prime factorsprime factorization of 2205is 801 a prime numberprime factorization 162common multiples of 8 and 10what are the prime factorization of 80what is the prime factorization of 80108 as a product of prime factors12x multiplication tableprime factor of 54prime factorization of 39prime factorization of 243prime factor of 108what are the prime factors of 72what is the prime factorization of 192what is the prime factorization of 675prime factorization of 231whats the prime factorization of 1620x multiplication tablethe prime factorization of 75whats the prime factorization of 81prime factorization of 89100-369x tableprime factorization for 19645 prime factorizationfind the prime factorization of 28multiplication table upto 30prime factorization 77lcm of 3 7 and 10what is the prime factorization of 328is 27 a prime number or a composite numberwhat is the greatest common factor of 48 and 64what are the prime factors of 125multiplication table of 42prime factorization of 39what is the prime factorization of 225whats the prime factorization of 144what is the greatest common factor of 64