The **gcf of 6 and 77** is the largest positive integer that divides the numbers 6 and 77 without a remainder. Spelled out, it is the greatest common factor of 6 and 77. Here you can find the gcf of 6 and 77, 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 6 and 77, but also that of three or more integers including six and seventy-seven for example. Keep reading to learn everything about the gcf (6,77) and the terms related to it.

## What is the GCF of 6 and 77

If you just want to know *what is the greatest common factor of 6 and 77*, it is **1**. Usually, this is written as

**gcf(6,77) = 1**

The gcf of 6 and 77 can be obtained like this:

- The factors of 6 are 6, 3, 2, 1.
- The factors of 77 are 77, 11, 7, 1.
- The
*common*factors of 6 and 77 are 1, intersecting the two sets above. - In the intersection factors of 6 ∩ factors of 77 the
*greatest*element is 1. - Therefore, the
**greatest common factor of 6 and 77 is 1**.

Taking the above into account you also know how to find *all* the common factors of 6 and 77, not just the greatest. In the next section we show you how to calculate the gcf of six and seventy-seven by means of two more methods.

## How to find the GCF of 6 and 77

The greatest common factor of 6 and 77 can be computed by using the least common multiple aka lcm of 6 and 77. This is the easiest approach:

Alternatively, the gcf of 6 and 77 can be found using the prime factorization of 6 and 77:

- The prime factorization of 6 is: 2 x 3
- The prime factorization of 77 is: 7 x 11
- The prime factors and multiplicities 6 and 77 have in common are: 1
- 1 is the gcf of 6 and 77
- gcf(6,77) = 1

In any case, the easiest way to compute the gcf of two numbers like 6 and 77 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 6,77. The calculation is conducted automatically.

## Use of GCF of 6 and 77

What is the greatest common factor of 6 and 77 used for? Answer: It is helpful for reducing fractions like 6 / 77. Just divide the nominator as well as the denominator by the gcf (6,77) to reduce the fraction to lowest terms.

\frac{6}{77} = \frac{\frac{6}{1}}{\frac{77}{1}} = \frac{6}{77}.

## Properties of GCF of 6 and 77

The most important properties of the gcf(6,77) are:

- Commutative property: gcf(6,77) = gcf(77,6)
- Associative property: gcf(6,77,n) = gcf(gcf(77,6),n) n\neq 0 \thinspace\in\thinspace\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 6 and 77 is 1. In common notation: gcf (6,77) = 1.

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

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