GCF of 14 and 49


The gcf of 14 and 49 is the largest positive integer that divides the numbers 14 and 49 without a remainder. Spelled out, it is the greatest common factor of 14 and 49. Here you can find the gcf of 14 and 49, 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 14 and 49, but also that of three or more integers including fourteen and forty-nine for example. Keep reading to learn everything about the gcf (14,49) and the terms related to it.

What is the GCF of 14 and 49

If you just want to know what is the greatest common factor of 14 and 49, it is 7. Usually, this is written as

gcf(14,49) = 7

The gcf of 14 and 49 can be obtained like this:

  • The factors of 14 are 14, 7, 2, 1.
  • The factors of 49 are 49, 7, 1.
  • The common factors of 14 and 49 are 7, 1, intersecting the two sets above.
  • In the intersection factors of 14 ∩ factors of 49 the greatest element is 7.
  • Therefore, the greatest common factor of 14 and 49 is 7.

Taking the above into account you also know how to find all the common factors of 14 and 49, not just the greatest. In the next section we show you how to calculate the gcf of fourteen and forty-nine by means of two more methods.

How to find the GCF of 14 and 49

The greatest common factor of 14 and 49 can be computed by using the least common multiple aka lcm of 14 and 49. This is the easiest approach:

gcf (14,49) = $\frac{14 \times 49}{lcm(14,49)} = \frac{686}{98}$ = 7

Alternatively, the gcf of 14 and 49 can be found using the prime factorization of 14 and 49:

  • The prime factorization of 14 is: 2 x 7
  • The prime factorization of 49 is: 7 x 7
  • The prime factors and multiplicities 14 and 49 have in common are: 7
  • 7 is the gcf of 14 and 49
  • gcf(14,49) = 7

In any case, the easiest way to compute the gcf of two numbers like 14 and 49 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 14,49. The calculation is conducted automatically.

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

Use of GCF of 14 and 49

What is the greatest common factor of 14 and 49 used for? Answer: It is helpful for reducing fractions like 14 / 49. Just divide the nominator as well as the denominator by the gcf (14,49) to reduce the fraction to lowest terms.

$\frac{14}{49} = \frac{\frac{14}{7}}{\frac{49}{7}} = \frac{2}{7}$.

Properties of GCF of 14 and 49

The most important properties of the gcf(14,49) are:

  • Commutative property: gcf(14,49) = gcf(49,14)
  • Associative property: gcf(14,49,n) = gcf(gcf(49,14),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 14 and 49 is 7. In common notation: gcf (14,49) = 7.

If you have been searching for gcf 14 and 49 or gcf 14 49 then you have come to the correct page, too. The same is the true if you typed gcf for 14 and 49 in your favorite search engine.

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

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