100 LearnersLast updated on May 26th, 2025
Factors of 2013
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 2013, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2013?
The numbers that divide 2013 evenly are known as factors of 2013.
A factor of 2013 is a number that divides the number without a remainder.
The factors of 2013 are 1, 3, 11, 33, 61, 183, 671, and 2013.
Negative factors of 2013: -1, -3, -11, -33, -61, -183, -671, and -2013.
Prime factors of 2013: 3, 11, and 61.
Prime factorization of 2013: 3 × 11 × 61.
The sum of factors of 2013: 1 + 3 + 11 + 33 + 61 + 183 + 671 + 2013 = 2976
How to Find Factors of 2013?
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 2013. Identifying the numbers which are multiplied to get the number 2013 is the multiplication method.
Step 1: Multiply 2013 by 1, 2013 × 1 = 2013.
Step 2: Check for other numbers that give 2013 after multiplying
3 × 671 = 2013
11 × 183 = 2013
33 × 61 = 2013
Therefore, the positive factor pairs of 2013 are: (1, 2013), (3, 671), (11, 183), (33, 61).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 a simple division method
Step 1: Divide 2013 by 1, 2013 ÷ 1 = 2013.
Step 2: Continue dividing 2013 by the numbers until the remainder becomes 0.
2013 ÷ 1 = 2013
2013 ÷ 3 = 671
2013 ÷ 11 = 183
2013 ÷ 33 = 61
Therefore, the factors of 2013 are: 1, 3, 11, 33, 61, 183, 671, 2013.
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 2013 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2013 ÷ 3 = 671
671 ÷ 11 = 61
61 ÷ 61 = 1
The prime factors of 2013 are 3, 11, and 61.
The prime factorization of 2013 is: 3 × 11 × 61.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 2013 is divided by 3 to get 671.
Step 2: Now divide 671 by 11 to get 61.
Step 3: Here, 61 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 2013 is: 3 × 11 × 61.
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 2013: (1, 2013), (3, 671), (11, 183), and (33, 61).
Negative factor pairs of 2013: (-1, -2013), (-3, -671), (-11, -183), and (-33, -61).
Common Mistakes and How to Avoid Them in Factors of 2013
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 2013, 1 and 2013 are also factors.
Factors of 2013 Examples
Problem 1
A charity event collected 2013 canned goods and wants to distribute them evenly among 3 shelters. How many cans will each shelter receive?
Each shelter will receive 671 cans.
Explanation
To divide the cans equally, we need to divide the total cans by the number of shelters.
2013/3 = 671
Problem 2
A rectangular banner has a length of 33 meters and a total area of 2013 square meters. Find the width.
61 meters.
Explanation
To find the width of the banner, we use the formula,
Area = length × width
2013 = 33 × width
To find the value of width, we need to shift 33 to the left side.
2013/33 = width
Width = 61.
Problem 3
There are 11 groups and 2013 students. How many students will be in each group?
Each group will have 183 students.
Explanation
To find the students in each group, divide the total number of students by the groups.
2013/11 = 183
Problem 4
In a library, there are 2013 books and 61 shelves. How many books will be on each shelf?
There are 33 books on each shelf.
Explanation
Dividing the total books by the total shelves, we will get the number of books on each shelf.
2013/61 = 33
Problem 5
A company produced 2013 widgets and wants to distribute them evenly among its 671 employees. How many widgets will each employee receive?
Each employee will receive 3 widgets.
Explanation
Divide the total widgets by the number of employees.
2013/671 = 3
FAQs on Factors of 2013
1.What are the factors of 2013?
2.Mention the prime factors of 2013.
3.Is 2013 a multiple of 11?
4.Mention the factor pairs of 2013?
5.What is the square of 2013?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 2013?
7.What are some fun ways kids in Bahrain can practice Factors of 2013 with numbers?
8.What role do numbers and Factors of 2013 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 2013 skills?
Important Glossaries for Factors of 2013
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2013 are 1, 3, 11, 33, 61, 183, 671, and 2013.
- Prime factors: The factors which are prime numbers. For example, 3, 11, and 61 are prime factors of 2013.
- 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 2013 are (1, 2013), (3, 671), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 2013 is 3 × 11 × 61.
- Multiplication method: A method to find factors by identifying pairs of numbers multiplied to give the original number. For example, using pairs like (3, 671) to find factors of 2013.
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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.
