Mathematics, Algebra and Function, Operations (+, -, x, /, etc.)

Grade 5- 8

### Objective

Students will learn about factors and prime factorization.

### Directions

**Factors**

A factor is one of two or more numbers that are multiplied together. The factors of 36 are the following: (1, 36) (2, 18) (3, 12) (4, 9) (6, 6) or (1, 2, 3, 4, 6, 9, 12, 18, 36).
The number 1 is always a factor of any number.
The number itself, such as 36, is always a factor.
A prime number is a counting number which has only 1 and itself for factors. For example, 7 is a prime number because the only factors are 1 and 7.
A composite number is a counting number which has factors other than 1 and itself. It has three or more factors. For example, 12 is a composite number because the factors are 1, 2, 3, 4, 6, and 12.

**Prime Factors and Prime Factorization**

The prime factors of a number are all of the factors of a number which are prime numbers. For example, the prime factors of 36 are 2 and 3. You can use a factor tree to determine the prime factors of a number:

36

/\

4 9

/\ /\

2 2 3 3

Exponents can be used to express 36 as a product of prime factors. The prime factorization of 36 is the following: 36 = 2 x 2 x 3 x 3 or 36 = 22 x 32

**Algebraic Factors**

An expression in algebra has slightly different terms for factors. Letters are called literal factors. Numbers are called numerical factors.

*Sample A*

Name the numerical and literal factors of this expression: 4abc.

Numerical factors: (4) --- Literal factors: (a, b, c)

*Sample B*

Name the numerical and literal factors of this expression: 2ab 9xy.

Numerical factors: (2, 9) --- Literal factors: (a, b, x, y)

Any factor or factors in an algebraic term is called the coefficient of the product of the remaining factors.

*Sample A*

Name the numerical and literal coefficients of this expression: 4abc.

Numerical coefficient: (4) --- Literal coefficient: (abc)

*Sample B*

Name the numerical and literal coefficients of this expression: 34xyz.

Numerical coefficient: (34) --- Literal coefficient: (xyz)

(Note: In a term such as abx, where there is no number, the numerical coefficient is always 1.)
### Resources

- copies of the activity pages for the students