100 LearnersLast updated on May 26th, 2025
Factors of 2028
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 2028, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2028?
The numbers that divide 2028 evenly are known as factors of 2028.
A factor of 2028 is a number that divides the number without a remainder.
The factors of 2028 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 169, 338, 507, 676, 1014, and 2028.
Negative factors of 2028: -1, -2, -3, -4, -6, -12, -13, -26, -39, -52, -78, -156, -169, -338, -507, -676, -1014, and -2028.
Prime factors of 2028: 2, 3, and 13.
Prime factorization of 2028: 2² × 3 × 13².
The sum of factors of 2028: 1 + 2 + 3 + 4 + 6 + 12 + 13 + 26 + 39 + 52 + 78 + 156 + 169 + 338 + 507 + 676 + 1014 + 2028 = 5074
How to Find Factors of 2028?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 2028. Identifying the numbers which are multiplied to get the number 2028 is the multiplication method.
Step 1: Multiply 2028 by 1, 2028 × 1 = 2028.
Step 2: Check for other numbers that give 2028 after multiplying
2 × 1014 = 2028
3 × 676 = 2028
4 × 507 = 2028
6 × 338 = 2028
12 × 169 = 2028
13 × 156 = 2028
26 × 78 = 2028
39 × 52 = 2028
Therefore, the positive factor pairs of 2028 are: (1, 2028), (2, 1014), (3, 676), (4, 507), (6, 338), (12, 169), (13, 156), (26, 78), (39, 52).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 2028 by 1, 2028 ÷ 1 = 2028.
Step 2: Continue dividing 2028 by the numbers until the remainder becomes 0.
2028 ÷ 1 = 2028
2028 ÷ 2 = 1014
2028 ÷ 3 = 676
2028 ÷ 4 = 507
2028 ÷ 6 = 338
2028 ÷ 12 = 169
2028 ÷ 13 = 156
2028 ÷ 26 = 78
2028 ÷ 39 = 52
Therefore, the factors of 2028 are: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 169, 338, 507, 676, 1014, 2028.
Prime Factors and Prime Factorization
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 2028 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2028 ÷ 2 = 1014
1014 ÷ 2 = 507
507 ÷ 3 = 169
169 ÷ 13 = 13
13 ÷ 13 = 1
The prime factors of 2028 are 2, 3, and 13.
The prime factorization of 2028 is: 2² × 3 × 13².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 2028 is divided by 2 to get 1014.
Step 2: Now divide 1014 by 2 to get 507.
Step 3: Then divide 507 by 3 to get 169.
Step 4: Divide 169 by 13 to get 13. Here, 13 is the smallest prime number, which cannot be divided anymore.
So, the prime factorization of 2028 is: 2² × 3 × 13².
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 2028: (1, 2028), (2, 1014), (3, 676), (4, 507), (6, 338), (12, 169), (13, 156), (26, 78), (39, 52).
Negative factor pairs of 2028: (-1, -2028), (-2, -1014), (-3, -676), (-4, -507), (-6, -338), (-12, -169), (-13, -156), (-26, -78), (-39, -52).
Common Mistakes and How to Avoid Them in Factors of 2028
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 2028, 1 and 2028 are also factors.
Factors of 2028 Examples
Problem 1
There are 169 students and 2028 candies. How will they divide them equally?
They will get 12 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
2028 ÷ 169 = 12
Problem 2
A rectangular garden has a length of 39 meters and a total area of 2028 square meters. Find the width.
52 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
2028 = 39 × width
To find the value of width, we need to shift 39 to the left side.
2028 ÷ 39 = width
Width = 52.
Problem 3
There are 52 crates and 2028 apples. How many apples will be in each crate?
Each crate will have 39 apples.
Explanation
To find the apples in each crate, divide the total apples by the crates.
2028 ÷ 52 = 39
Problem 4
In a library, there are 2028 books and 78 shelves. How many books are there on each shelf?
There are 26 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
2028 ÷ 78 = 26
Problem 5
2028 pieces of art need to be displayed in 4 galleries. How many pieces will go in each gallery?
Each gallery will have 507 pieces of art.
Explanation
Divide the total pieces by the number of galleries.
2028 ÷ 4 = 507
FAQs on Factors of 2028
1.What are the factors of 2028?
2.Mention the prime factors of 2028.
3.Is 2028 a multiple of 13?
4.Mention the factor pairs of 2028.
5.What is the cube of 2028?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 2028?
7.What are some fun ways kids in Bahrain can practice Factors of 2028 with numbers?
8.What role do numbers and Factors of 2028 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 2028 skills?
Important Glossaries for Factor of 2028
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2028 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 169, 338, 507, 676, 1014, and 2028.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are the prime factors of 2028.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 2028 are (1, 2028), (2, 1014), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, 2028 can be expressed as 2² × 3 × 13².
- Multiple: A multiple is a product of a number and an integer. For example, 2028 is a multiple of 13.
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About BrightChamps in Bahrain
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.
