Factors – Definition, Steps to Find, Examples

Key Concepts

• Factor pairs
• Grouping and finding factors

Understand factors  

What is a factor? 

Multiplying two whole numbers gives a product. The numbers that we multiply are the factors of the product.   

Example:  3 × 5 = 15. Therefore, 3 and 5 are the factors of 15. 

This also means: 

A factor divides a number completely without leaving any remainder. 

Factor pairs 

Factors are often given as pairs of numbers, which multiply together to give the original number. These are called factor pairs.  

For example, the factor pairs of 20 are:  

4. 1 and 20 

5. 2 and 10 

6. 4 and 5 

Example 1:  

The English teacher is trying to arranged chairs in a rectangular array for group discussion. How many different ways can the chairs be arranged into a rectangular array? 

6 chairs.   

Solution: 

1 row of 6 chairs. 6 rows of 1 chair. 

2 rows of 3 chairs. 

3 rows of 2 chairs.  

There are 4 possible ways the 6 chairs can be arranged. 

Example 2: 

A gardener wants to plant 20 plants. What are the different ways he can plant the plants into a rectangular array? 

Solution: 

1 row of 20 plants. 

20 rows of 1 plant each. 

4 rows of 5 plants. 

5 rows of 4 plants. 

2 rows of 10 plants. 

10 rows of 2 plants. 

Grouping and Finding Factors  

Factor: 

Numbers we can multiply together to get another number. 

Example1:  

2 and 3 are factors of 6, because 2 × 3 = 6 

Example 2: 

Maria wants to arrange her 18 photo frames in an equal size of group. Find all the ways Maria can arrange her photo frames on the wall. 

Solution:  

 1 group of 18. 

18 groups of 1. 

[Text Wrapping Break] 

Ria can arrange 1 group of 18 figures or 18 groups of 1 figure. 

1 x 18 =18 

18 x 1 = 18  

9 groups of 2. 

2 groups of 9 

Ria can arrange 9 groups of 2 figures or 2 groups of 9 figures. 

2 x 9 =18 

9 x 2 = 18 

3 groups of 6. 

6 groups of 3 

Ria can arrange 3 groups of 6 figures or 6 groups of 3 figures. 

6 x 3 =18 

3 x 6 = 18 

The factor pairs for 18 are 1 and 18, 2 and 9, 3 and 6. 

Example 2: 

Robert wants to arrange toy cars in equal size of groups. What are all the ways in which Robert can arrange his toy cars? 

10 toy cars. 

Solution:  

1 group of 10. 

10 groups of 1  

1 x 10 = 10 

10 x 1 = 10 

5 groups of 2 

2 groups of 5  

      2 x 5 = 10 

      5 x 2 = 10 

The factor pairs for 10 are 1 and 10, 2 and 5.

Exercise:

1. Find all of the factor pairs for each number. You can use grids to help.
   1. 14
   2. 18
2. Find the factors of each number.
   1. 25
   2. 30
3. Write the factor of each number. Use counters to help as needed.
   1. 49
   2. 35

4. Any number that has 9 as a factor and also 3 as a factor. Why is this?
5. Write the factor pairs for each number.
   1. 19
   1. 1 and _____
   2. 16
   1. _______ and _______
   2. _______ and _______.

6. Write all the factors of 20.
7. What do you observe about the number of possible arrays and the number of factors of 28?
8. Kelvin has 18 plants. He wants to plant all of the plants in equal rows in his garden. What are the different ways in which Kelvin can arrange the flowers in equal rows?
9. Use the grid to find two numbers that have 2 and 4 as a factor.  

What have we learned:

• Understand factors.
• Understand pair of factors.
• Understand how to find the factors for given numbers.
• Understand how to do grouping and find factors.

Concept Map