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The GCF calculator finds the greatest common factor between two and six numbers. The phrase greatest common factor calculator may be used interchangeably, as that's what the GCF acronym stands for. First we need to know what is GCF and how to find the greatest common factor.

The GCF is the largest factor that is present between a set of numbers. This is also known as the *greatest common divisor* or GCD. This is important in applications of mathematics such as simplifying polynomials where often it's important to pull out common factors. Next we need to know how to find the GCF.

Suppose we want to get the GCF between `42`

, `54`

and `72`

. Follow the following steps:

- Get the prime factorization of each number, which gives us
`42 = 2 * 3 * 7`

,`54 = 2 * 3 * 3 * 3`

and`72 = 2 * 2 * 2 * 3 * 3`

. - Look for the factors that each set has in common. In this case that is
`2 and 3`

. - Get the highest power of each factor, which is just one
`2`

and one`3`

. - Multiply the factors. The answer in this case is
`2 * 3 = 6`

. - Check your result using the GCF calculator.

The way to find the GCF is to break each number down into its prime factors using a factor calculator or the prime factorization calculator. Next we check for all factors between the numbers and multiply the highest power of each factor. The result the the greatest common factor. An example will be worked by hand in the next section, with step by step instructions.

Another concept closely related is the least common multiple. To find the least common multiple, we use much that same process as finding the GCF. Once we get the numbers down to the prime factorization, we look for the *smallest* power of each factor, as opposed to the largest power. Then we multiply the highest powers and the result is the least common multiple of LCM. This can be done by hand or with the use of the LCM calculator.

In the previous example, the highest power of the factor `2`

is `2 * 2 * 2`

. The highest power of `3`

is `3 * 3 * 3`

and the highest power of `7`

is `7`

. So the LCM would be `2 * 2 * 2 * 3 * 3 * 3 * 7 = 1512`

.