## What is an Algebraic Factor?

A factor is a number that makes another number as a product. The word factor comes from a Latin root that means “make” or “do,” and is related to the concept of a factory. A factor can be a number, a polynomial, or a summand. It can also be a term, like 2x+3y or a coefficient, or a constant.

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### Factors and Primes

In algebra, numbers that are expressed as products of whole numbers are called factors. These products are sometimes known as primes. For example, 12 has two factors, 3 and 4. A product of a number and a prime is called a factor of the number; the product of a prime and a non-prime is called a multiple or a divisor of the number.

There are a few different ways to express these products, each of which has its own definition. But one of the most important is to say that a product of a number and a factor is a repeated sum. This is because a repeated sum consists of a number of summands (i.e., a repeated addition), and each of those summands has its own exponent.

For a repeated product, the exponent is the same for each of the factors. The base of the power is the same for each of the factors, too. The base is the number that can be rounded to the next power.

### Finding the Greatest Common Factor

To find the greatest common factor of an expression, we need to look at all its terms. We can do this by dividing each of the terms into its number part and each of the variable parts. We can use the largest of these parts to determine the greatest common factor.

It’s easier to do this one variable at a time, but it does take some practice and it is worth the effort. We might try to find the largest factor for each of the first five terms, and then we can work our way down.

### What Are the Definitions of Algebraic Terms?

The words term and factor are used interchangeably in algebra. A term is a number, a polynomial, a summand, or an arithmetic operation. It can also be a factor, like 2x+3y or x(x+2), or it can be a coefficient, like z to the fifth.

### What Are the Meanings of Terms, Coefficients and Constants?

A term in an algebraic expression is a number, a variable, a polynomial, e.g., 2x+3y or a summand, like 5a2-2ab+b3. It can also be a coefficient, like z to a fifth. It can also be a constant, like x squared.

### What Are the Meanings of Factor and Variable?

A factor in an expression is a variable, a polynomial, or an arithmetic operation. A variable can be any number that takes on a numerical value.

### What Are the Definitions of Terms, Coefficients and Constants?

A term in an algebraic expression is mainly a number, a polynomial, an arithmetic operation, or a summand. It may also be a coefficient, like z a fifth or a constant, like x squared. A term can have more than one constant term, and a constant can be any number that does not change its value.