# How do you find the greatest common factor with variables and exponents?

## How do you find the greatest common factor with variables and exponents?

Finding the Greatest Common Factor (GCF): To find the GCF of two expressions:

1. Factor each coefficient into primes. Write all variables with exponents in expanded form.
2. List all factors—matching common factors in a column.
3. Bring down the common factors that all expressions share.
4. Multiply the factors as in (Figure).

## How do u find the greatest common factor?

To find the GCF of a set of numbers, list all the factors of each number. The greatest factor appearing on every list is the GCF. For example, to find the GCF of 6 and 15, first list all the factors of each number. Because 3 is the greatest factor that appears on both lists, 3 is the GCF of 6 and 15.

How do you find the greatest common factor?

Here’s how to find the GCF of a set of numbers using prime factorization:

1. List the prime factors of each number.
2. Circle every common prime factor — that is, every prime factor that’s a factor of every number in the set.
3. Multiply all the circled numbers. The result is the GCF.

How do you determine the greatest common factor from a polynomial?

How to Find a Greatest Common Factor in a Polynomial

1. Break down every term into prime factors.
2. Look for factors that appear in every single term to determine the GCF.
3. Factor the GCF out from every term in front of parentheses and group the remnants inside the parentheses.
4. Multiply each term to simplify.

### How do you use the greatest common factor?

The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.

How do you find the least common multiple?

Find the least common multiple (LCM) of two numbers by listing multiples

1. List the first several multiples of each number.
2. Look for multiples common to both lists.
3. Look for the smallest number that is common to both lists.
4. This number is the LCM.

How to find the greatest factor and least common factor?

Then, we find the greatest factor that is common to all the numbers. The least common multiple is the smallest multiple shared between two numbers. To find the least common multiple, we list the multiples of each number, and then look for the first number that they have in common. To unlock this lesson you must be a Study.com Member.

#### How to calculate the least common factor LCM?

Multiply all prime factors together while repeating each factor by whichever exponent level is highest for that prime cake / ladder: Divide numbers by prime numbers as long as two numbers remain evenly divisible by that number then carry down any numbers that are not divsible by that factor. multiply the factors by the remainders to obtain the LCM.

#### Which is the greatest factor of both numbers?

The greatest common factor of two numbers is the greatest integer that is a factor of both numbers. For example, the GCF of and is . Notice that and have a factor of and a factor of in common, and so the greatest common factor of and is .

How to find the greatest common factor of two monomials?

Notice that and have a factor of and a factor of in common, and so the greatest common factor of and is . The process is similar when you are asked to find the greatest common factor of two or more monomials. Simply write the complete factorization of each monomial and find the common factors. The product of all the common factors will be the GCF.