Arithmetic Worksheets

Practice and master arithmetic with our helpful walkthroughs and downloadable practice worksheets from our team of elite math educators.

What is a factor

By Dana Valdez

Learn about what a factor is and how to use it to solve problems. Find the definition, example problems, and practice problems at Thinkster Math.

Why is this concept useful?

Factors can be described as numbers that multiply to equal a product. You can also describe a factor as a number that divides evenly into another number, with no remainder. Factors are used in multiplication, division, simplifying fractions, factorization, and many other mathematical concepts.

Where does this concept fit into the curriculum?

Grade 3

What is a factor?

We can find the factors of 1, 2, and 3 digit numbers. To find the factors of a number, you find which numbers multiply to equal a given number. For example, the factors of 5 are 1 and 5 because the only numbers that multiply to equal 5 are 1 and 5. The factors of 4 are 1, 2, and 4 because 1 x 4 = 4 and 2 x 2 = 4.

When working with larger numbers, such as 100, you should start with the lowest numbers and check if they can be divided evenly, with no remainder, into 100.

For example

100÷1=100100\div 1=100

so 1 and 100 are factors

100÷2=50100\div 2=50

so 2 and 50 are factors

100÷3=33 R 1100\div 3=33\ R\ 1

As there is a reminder of 1, 3 is not a factor of 100

100÷4=25100\div 4=25

so 4 and 25 are factors

100÷5=20100\div 5=20

so 5 and 20 are factors

100÷6=16 R 4100\div 6=16\ R\ 4

As there is a reminder of 4, 6 is not a factor of 100

100÷10=10100\div 10=10

so 10 is a factor

Usually, you list the factors in order from least to greatest when you answer the question. The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, and 100.


Sample Math Problems

Question:

What are the factors of 9?


Answer:

1 x 9 = 9

3 x 3 = 9

The factors of 9 are: 1, 3, and 9.


Question:

What are the factors of 48?

Answer:

1 x 48 = 48

2 x 24 = 48

3 x 16 = 48

4 x 12 = 48

6 x 8 = 48

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Question:

What are the factors of 112?

Answer:

1 x 112 = 112

2 x 56 = 112

4 x 28 = 112

7 x 16 = 112

8 x 14 = 112

The factors of 112 are: 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.


Question:

What are the factors of 500?

Answer:

1 x 500 = 500

2 x 250 = 500

4 x 125 = 500

5 x 100 = 500

10 x 50 = 500

The factors of 500 are: 1, 2, 4, 5, 10, 50, 100, 125, 250, and 500.


Download FREE Math Resources

Take advantage of our free downloadable resources and study materials for at-home learning.

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Practice Math Problems

Question 1:

What are the factors of 8?

Question 2:

What are the factors of 12?

Question 3:

What are the factors of 45?

Question 4:

What are the factors of 396?

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