The **gcf of 100 and 99** is the largest positive integer that divides the numbers 100 and 99 without a remainder. Spelled out, it is the greatest common factor of 100 and 99. Here you can find the gcf of 100 and 99, 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 100 and 99, but also that of three or more integers including hundred and ninety-nine for example. Keep reading to learn everything about the gcf (100,99) and the terms related to it.

## What is the GCF of 100 and 99

If you just want to know *what is the greatest common factor of 100 and 99*, it is **1**. Usually, this is written as

**gcf(100,99) = 1**

The gcf of 100 and 99 can be obtained like this:

- The factors of 100 are 100, 50, 25, 20, 10, 5, 4, 2, 1.
- The factors of 99 are 99, 33, 11, 9, 3, 1.
- The
*common*factors of 100 and 99 are 1, intersecting the two sets above. - In the intersection factors of 100 ∩ factors of 99 the
*greatest*element is 1. - Therefore, the
**greatest common factor of 100 and 99 is 1**.

Taking the above into account you also know how to find *all* the common factors of 100 and 99, not just the greatest. In the next section we show you how to calculate the gcf of hundred and ninety-nine by means of two more methods.

## How to find the GCF of 100 and 99

The greatest common factor of 100 and 99 can be computed by using the least common multiple aka lcm of 100 and 99. This is the easiest approach:

Alternatively, the gcf of 100 and 99 can be found using the prime factorization of 100 and 99:

- The prime factorization of 100 is: 2 x 2 x 5 x 5
- The prime factorization of 99 is: 3 x 3 x 11
- The prime factors and multiplicities 100 and 99 have in common are: 1
- 1 is the gcf of 100 and 99
- gcf(100,99) = 1

In any case, the easiest way to compute the gcf of two numbers like 100 and 99 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 100,99. The calculation is conducted automatically.

## Use of GCF of 100 and 99

What is the greatest common factor of 100 and 99 used for? Answer: It is helpful for reducing fractions like 100 / 99. Just divide the nominator as well as the denominator by the gcf (100,99) to reduce the fraction to lowest terms.

\frac{100}{99} = \frac{\frac{100}{1}}{\frac{99}{1}} = \frac{100}{99}.

## Properties of GCF of 100 and 99

The most important properties of the gcf(100,99) are:

- Commutative property: gcf(100,99) = gcf(99,100)
- Associative property: gcf(100,99,n) = gcf(gcf(99,100),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 100 and 99 is 1. In common notation: gcf (100,99) = 1.

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

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