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367 LearnersLast updated on December 17, 2025
Factors of 12
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.
Mistake 1
Ignoring the Negative Factors.
Always remember that each positive factor has a consistent negative factor. For example, factors of 12 are ±1, ±2, ±3, ±4, ±6, ±12.
Mistake 2
Not Checking Divisibility Properly
In some cases, children might wrongly assume that a number cannot be divided further. For example, they may assume that 8 isn't a factor of 24. However, this calculation proves otherwise: 24 ÷ 8 = 3 (no remainder). So 8 is a factor of 24. To avoid this error, always check divisibility.
Mistake 3
Avoiding Larger Factors
Sometimes, students may stop the calculation, after identifying the smaller factors, whereas forget to identify the corresponding larger factors. For example: they might list 1, 2, 3, 4, and forget the larger factors 6, 8, 12, and 24. The solution to these mistakes is to try to divide numbers systematically, and also pair them with larger factors.
Examples on Factors of 12
Problem 1
Miya wants to distribute 108 chocolates equally among 36 friends. How many candies does each friend get?
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
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?
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
Problem 3
What is the GCF of 108 and 72?
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.
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?
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.
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?
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.
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?
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.
FAQs on Factors of 12
1.What factors are multiplied to get 108?
2.Is 108 a composite number?
3.What is 108 divisible by?
4.Is 108 a perfect square?
5.What is the prime factor of 108?
6.How many factors does 12 have?
7.What is the smallest factor of 12?
8.What is the largest factor of 12?
9.Which factors of 12 add up to 13?
10.How many even factors does 12 have?
11.What are the odd factors of 12?
12.What is the sum of all the factors of 12?
Important Terms Related to Factors of 12
- Factors: Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6, therefore, 1, 2, 3, and 6 are the factors of 6.
- Prime Factors: Prime factors of the numbers that multiply together to give a certain product. For 108, the prime factors are 2 and 3.
- Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).
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.
