GCF of 55 and 11

The gcf of 55 and 11 is the largest positive integer that divides the numbers 55 and 11 without a remainder. Spelled out, it is the greatest common factor of 55 and 11. Here you can find the gcf of 55 and 11, 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 55 and 11, but also that of three or more integers including fifty-five and eleven for example. Keep reading to learn everything about the gcf (55,11) and the terms related to it.

What is the GCF of 55 and 11

If you just want to know what is the greatest common factor of 55 and 11, it is 11. Usually, this is written as

gcf(55,11) = 11

The gcf of 55 and 11 can be obtained like this:

• The factors of 55 are 55, 11, 5, 1.
• The factors of 11 are 11, 1.
• The common factors of 55 and 11 are 11, 1, intersecting the two sets above.
• In the intersection factors of 55 ∩ factors of 11 the greatest element is 11.
• Therefore, the greatest common factor of 55 and 11 is 11.

Taking the above into account you also know how to find all the common factors of 55 and 11, not just the greatest. In the next section we show you how to calculate the gcf of fifty-five and eleven by means of two more methods.

How to find the GCF of 55 and 11

The greatest common factor of 55 and 11 can be computed by using the least common multiple aka lcm of 55 and 11. This is the easiest approach:

gcf (55,11) = $\frac{55 \times 11}{lcm(55,11)} = \frac{605}{55}$ = 11

Alternatively, the gcf of 55 and 11 can be found using the prime factorization of 55 and 11:

• The prime factorization of 55 is: 5 x 11
• The prime factorization of 11 is: 11
• The prime factors and multiplicities 55 and 11 have in common are: 11
• 11 is the gcf of 55 and 11
• gcf(55,11) = 11

In any case, the easiest way to compute the gcf of two numbers like 55 and 11 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 55,11. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 55 and 11

What is the greatest common factor of 55 and 11 used for? Answer: It is helpful for reducing fractions like 55 / 11. Just divide the nominator as well as the denominator by the gcf (55,11) to reduce the fraction to lowest terms.

$\frac{55}{11} = \frac{\frac{55}{11}}{\frac{11}{11}} = \frac{5}{1}$.

Properties of GCF of 55 and 11

The most important properties of the gcf(55,11) are:

• Commutative property: gcf(55,11) = gcf(11,55)
• Associative property: gcf(55,11,n) = gcf(gcf(11,55),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 55 and 11 is 11. In common notation: gcf (55,11) = 11.

If you have been searching for gcf 55 and 11 or gcf 55 11 then you have come to the correct page, too. The same is the true if you typed gcf for 55 and 11 in your favorite search engine.

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

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