Factors of 12
2026-02-28 01:24 Diff
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Last updated on December 17, 2025

A number that divides another number without leaving any remainder is called a factor of the given number. The concept of factors is applied in day-to-day life. They are useful in deciding the best time to schedule work shifts and events.

What are the Factors of 12?

Factors often come in pairs. There are several methods to figure them out, which you'll be learning about in a second.

For now let's just focus on the factors of 12, which are mentioned below:

Factor Type Values Positive Factors of 12 1, 2, 3, 4, 6, 12 Negative Factors of 12 -1, -2, -3, -4, -6, -12 Prime Factors of 12 2, 3 Prime Factorization of 12 2 × 2 × 3 = 2² × 3 The sum of the Factors of 12 28

How to Find the Factors of 12?

For finding factors, school kids use different methods for easy calculation. A few commonly used methods are as follows:

  • Use of Multiplication Method
  • Use of Division Method
  • Use of Prime Factors and Prime Factorization

So, here we discuss a detailed explanation of the following methods:
 

Finding Factors Using Multiplication Method

In the multiplication method, we will try to find out what numbers will multiply together, and give us the value 12. We will check the factors step by step:


Step 1: Start to multiply with numbers, which gives the value of 12.


Start with 1, and continue to multiply with other numbers. 


1 × 12 = 12
2 × 6 = 12
3 × 4 = 12


Step 2: After the calculation, we get these numbers, the factors of 12.


Step 3: The positive factor pairs of 12 found through multiplication are(1,12), (2,6), and (3,4)


Step 4: The negative factor pairs of 12 are (-1,-12), (-2,-6), and  (-3,-4)
 

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Finding Factors Using Division Method

Using this method, we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 108:


Step 1: Divide 108 by smaller numbers and see if there is any remainder. E.g., 108/1 = 108.

 
Step 2: We will continue in the same way and check for other numbers as well. For 108, the factors are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108. Because 108 can be divided evenly by these numbers.
 

Prime Factors and Prime Factorization

The prime factors of 108 are 2 and 3. The prime factors can be found using the methods given below:

  • Prime Factorization
  • Factor Tree

By Using Prime Factorization:  It is a method in which we break down a number into its prime factor. 


2 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.


108 ÷ 2 = 54
54  ÷ 2 = 27
27 ÷ 3 = 9
9  ÷ 3 = 3
3  ÷ 3 = 1


 The prime factorization of 108 is :


 108 = 22 × 33


Finally, using the prime factorization method, the prime factors of 108 are 2 and 3.
 

Prime Factors of 12

Prime Factorization of 12

Factor Tree

A factor tree is a visual representation of breaking a number into its prime factors. It is an easy and simple way to present the factors.


Step 1: 108 divided by 2 gives us the answer 54.


Step 2: Since 54 is not a prime number, it can be divided further.


108 ÷ 2 = 54
54  ÷ 2 = 27
27 ÷ 3 = 9
9  ÷ 3 = 3
3  ÷ 3 = 1 


The prime factorization of 108 is written below : 


  108 = 22 × 33

Factor Pairs of 12

The factors of 12 can be written in both positive and negative pairs. The table below represents the factor pairs of 12, where the product of each pair of numbers is equal to 12.

Positive Pair Factors of 12:

Factors Positive Pair Factors 1 × 12 = 12 1, 12 2 × 6 = 12 2, 6 3 × 4 = 12 3, 4

Since the product of two negative numbers is also positive, 12 also has negative pair factors.

Negative Pair Factors of 12:

Factors Negative Pair Factors −1 × −12 = 12 −1, −12 −2 × −6 = 12 −2, −6 −3 × −4 = 12 −3, −4

Common Mistakes and How to Avoid Them in Factors Of 108

Children tend to make mistakes while finding the factors of a number. Let us look at how to avoid those mistakes.
 

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Problem 1

Miya wants to distribute 108 chocolates equally among 36 friends. How many candies does each friend get?

Okay, lets begin

 Each friend will get 3 candies.

Explanation

The best way to distribute the chocolates equally among friends is to divide the total number of chocolates by the total number of friends. After the calculation, Miya finds the solution and each friend will get 3 candies.
108 ÷ 36 = 3
 

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Problem 2

Sonya plans to plant flowers in a garden. She wants to plant 108 flowers in rows, with 4 flowers in each row. So how many rows of flowers will there be?

Okay, lets begin

 Sonya can make 27 rows of flowers.
 

Explanation

The total number of flowers she wants in a row is 108 with 4 flowers in each row. To calculate the total number of flowers, divide the total number of flowers by the number of flowers in each row.


108 ÷ 4 = 27
 

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Problem 3

What is the GCF of 108 and 72?

Okay, lets begin

The GCF of 108 and 72 is 36.
 

Explanation

36 is the greatest common factor of 108 and 72. 


Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36.
The common factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.


GCF = 36.
 

Well explained 👍

Problem 4

At a Costco store in Dallas, a teacher buys 12 juice boxes to distribute equally among students in a science club. She wants to divide them into groups so that each group has the same number of juice boxes with none left over. What are all the possible group sizes she can use?

Okay, lets begin

1, 2, 3, 4, 6, 12

Explanation

To divide 12 juice boxes equally without leftovers, we look for numbers that divide 12 exactly.

Any number that divides 12 with no remainder is a factor of 12. Checking systematically gives the factors 1, 2, 3, 4, 6, and 12.

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Problem 5

A middle school in Chicago orders 12 NBA team jerseys for a basketball showcase. The coach wants to arrange them into equal rows for display. Which row arrangements are possible using all 12 jerseys?

Okay, lets begin

1, 2, 3, 4, 6, 12

Explanation

Each row arrangement must use all 12 jerseys evenly.

This means the number of rows must be a factor of 12. Dividing 12 by different whole numbers shows that 1, 2, 3, 4, 6, and 12 work without leaving extras.

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Problem 6

A pharmacy student in Boston is studying dosage packaging at CVS. A bottle contains 12 tablets, and the tablets must be packed into equal daily-dose strips. How many tablets can each strip contain without breaking any tablets?

Okay, lets begin

1, 2, 3, 4, 6, 12

Explanation

Since tablets cannot be broken, each strip must contain a number that divides 12 exactly.

The numbers that divide 12 with no remainder are its factors, which are 1, 2, 3, 4, 6, and 12.

Well explained 👍

FAQs on Factors of 12

1.What factors are multiplied to get 108?

These are pair factors. The pair factors of 108 are: (1,108), (2,54), (3,36), (4,27), (6,18), and (9,12)
 

2.Is 108 a composite number?

Yes, 108 is a composite number. It has more than two factors. Therefore, it is classified as a composite number.
 

3.What is 108 divisible by?

108 is divisible by numbers that can divide it completely. These numbers, known as factors of 108, are 1, 2, 3, 4, 6, 12, 18, 27, 36, 54, and 108.
 

4.Is 108 a perfect square?

5.What is the prime factor of 108?

108 has two prime factors. The prime factors of 108 are 2 and 3.
 

6.How many factors does 12 have?

The number 12 has 6 factors.


Factors are whole numbers that divide 12 evenly without leaving any remainder. These numbers come in pairs that multiply to give 12.

7.What is the smallest factor of 12?

The smallest factor of 12 is 1.


This is because 1 divides every whole number evenly and is always the smallest possible factor.

8.What is the largest factor of 12?

The highest factor of 12 is 12 itself.


Every number is always divisible by itself, making it the largest factor.

9.Which factors of 12 add up to 13?

The factors of 12 that add up to 13 are 1 and 12.


Both numbers divide 12 exactly, and their sum is 1 + 12 = 13.

10.How many even factors does 12 have?

The number 12 has 4 even factors.


Even factors are numbers divisible by 2. The even factors of 12 are 2, 4, 6, and 12.

11.What are the odd factors of 12?

The odd factors of 12 are 1 and 3.


Odd factors are numbers that are not divisible by 2 but still divide 12 evenly.

12.What is the sum of all the factors of 12?

The sum of all the factors of 12 is 28.


When you add all the factors—1, 2, 3, 4, 6, and 12—the total equals 28.

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.