# Arrays and factors

### Arrays and factors

#### Lessons

In this lesson, we will learn:

• Factors, Products, Multiplication Statements
• Writing a product for a given array
• Drawing arrays to find factors
• Using an array to describe the distributive property of multiplication

Notes:

Factors
• Numbers we can multiply to get another number
• Numbers we can multiply to get another number
• two numbers that we multiply together to get a certain product

Ex. 3 x 4 = 12

3 and 4 are both factors of 12 and 3 and 4 are a factor pair

$\quad$ 2 x 6 = 12

2 and 6 are also factors of 12, 2 and 6 are a factor pair

BUT be careful! 2 and 4 are not a factor pair of 12 even though they are both factors of 12 because:

2 x 4 DOES NOT EQUAL 12

Tips for finding factors
• Every number has 1 as a factor
• Every number has itself as a factor

Product
• The term product in this section is used for both an expression involving multiplication and the evaluation of that expression

$\qquad \qquad$ Ex. The product of 2 and 5 is: 2 x 5 and 10

Arrays
• An array is a diagram which represents a product
• You can draw an array with dots or with squares

Writing a product for a given array
The product is created by writing the number of rows times the number of columns
The product for the above array would be 2 x 3 or 6
• 1.
Products and Arrays
Write a product for each array
a)

b)

c)

d)

• 2.
Find Factors using Arrays
Draw an array to find the factors of
a)
12

b)
6

c)
7

• 3.
Arrays and the Distributive Property
1. Write a product for the entire diagram, the unshaded squares and the shaded squares
2. Write an equation for the entire diagram (using the distributive property)
a)

b)

• 4.
Rewriting products in expanded form
Rewrite each product in expanded form (rewrite as a sum)
a)
6 x 12

b)
3 x 128

c)
7 x 408

• 5.
Distributive Property of Multiplication (multiplying by 1-digit)
Use the distributive property to find the product:
a)
4 x 36

b)
3 x 825

c)
401 x 9

• 6.
Distributive Property of Multiplication (2-digit x 2-digit)
Use the distributive property to find the product:
a)
14 x 12

b)
65 x 34