7.4.1 Factors and Monomials

Factors and Monomials

Vocabulary and Rules

Factors: Two or more numbers that are multiplied to form a product

4 • 8 = 32

Factors Product

Draw

Draw on the image where the FACTORS and the PRODUCT is on the given equation.

Multiple Choice

In the equation 2 x 3 = 6, 6 is called the ___

• sum

• difference

• product

• quotient

Multiple Choice

In the equation 2 x 3 = 6, 3 is called a ___

• sum

• factor

• product

• quotient

Try some examples

■

Determine whether 138 is divisible by 2, 3, 5, 6, or 10

Number

Divisible?

Reason

2

Yes

The ones digit is 8 and 8 is divisible by 2

3

Yes

1+3+8 is 12, and 12 is divisible by 2

5

No

The ones digit is 8, not 0 or 5

6

Yes

138 is divisible by 2 and 3

10

No

The ones digit is no 0

So, 138 is divisible by 2, 3, and 6.

You can also use divisibility rules to find
factors of a number

■

List all the factors 82:
1 x 82

2 x 42

So the factors of 82 are 1, 2, 42, 82

■

List all the factors of 72:

1x72

6 x 12

2x36

7 x (nothing)

3x24

8 x 9

4x18

9 x 8 You can stop finding factors when the

numbers start repeating

5 x (nothing)

So the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Monomials

■

A monomial is a number, variable, or a product of a number and/or variable.

■

Example:

❖

4

Monomial because it’s a number

❖

Y

Monomial because it’s a variable

❖

-2 VK

Monomial because it’s a product of a number and variables

❖

2 + R

Not a monomial because it shows addition

❖

4c – 5

Not a monomial because it shows subtraction

❖

2 (v + k)

Not a monomial because both terms are added

Let’s Try Some Examples

Use divisibility rules to determine whether the number is divisible by 2, 3, 5, 6, or 10

1)

120

List the factors of given number

2) 90

Determine whether the expression is a monomial. Why or why not.

3) 110

4) b – c

5) xyz

Let’s Check Our Answers!

Use divisibility rules to determine whether the number is divisible by 2, 3, 5, 6, or 10

1)

120 Divisible by 2, 3, 5, 6, and 10

List the factors of given number

2) 90 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Determine whether the expression is a monomial. Why or why not.

3) 110

4) b – c

5) xyz

Yes, 110 is a number No, shows subtraction

Yes, shows product of variables