100 LearnersLast updated on May 26th, 2025
Factors of 2100
Factors are the numbers that divide any given number evenly without 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 2100, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2100?
The numbers that divide 2100 evenly are known as factors of 2100.
A factor of 2100 is a number that divides the number without remainder.
The factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, and 2100.
Negative factors of 2100: -1, -2, -3, -4, -5, -6, -7, -10, -12, -14, -15, -20, -21, -25, -28, -30, -35, -42, -50, -60, -70, -75, -84, -100, -105, -140, -150, -175, -210, -300, -350, -420, -525, -700, -1050, and -2100.
Prime factors of 2100: 2, 3, 5, and 7.
Prime factorization of 2100: 2² × 3 × 5² × 7.
The sum of factors of 2100: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 + 12 + 14 + 15 + 20 + 21 + 25 + 28 + 30 + 35 + 42 + 50 + 60 + 70 + 75 + 84 + 100 + 105 + 140 + 150 + 175 + 210 + 300 + 350 + 420 + 525 + 700 + 1050 + 2100 = 7938
How to Find Factors of 2100?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 2100. Identifying the numbers which are multiplied to get the number 2100 is the multiplication method.
Step 1: Multiply 2100 by 1, 2100 × 1 = 2100.
Step 2: Check for other numbers that give 2100 after multiplying
2 × 1050 = 2100
3 × 700 = 2100
4 × 525 = 2100
5 × 420 = 2100
6 × 350 = 2100
7 × 300 = 2100
10 × 210 = 2100
12 × 175 = 2100
14 × 150 = 2100
15 × 140 = 2100
20 × 105 = 2100
21 × 100 = 2100
25 × 84 = 2100
28 × 75 = 2100
30 × 70 = 2100
35 × 60 = 2100
42 × 50 = 2100
Therefore, the positive factor pairs of 2100 are: (1, 2100), (2, 1050), (3, 700), (4, 525), (5, 420), (6, 350), (7, 300), (10, 210), (12, 175), (14, 150), (15, 140), (20, 105), (21, 100), (25, 84), (28, 75), (30, 70), (35, 60), (42, 50).
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 as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 2100 by 1, 2100 ÷ 1 = 2100.
Step 2: Continue dividing 2100 by the numbers until the remainder becomes 0.
2100 ÷ 1 = 2100
2100 ÷ 2 = 1050
2100 ÷ 3 = 700
2100 ÷ 4 = 525
2100 ÷ 5 = 420
2100 ÷ 6 = 350
2100 ÷ 7 = 300
2100 ÷ 10 = 210
2100 ÷ 12 = 175
2100 ÷ 14 = 150
2100 ÷ 15 = 140
2100 ÷ 20 = 105
2100 ÷ 21 = 100
2100 ÷ 25 = 84
2100 ÷ 28 = 75
2100 ÷ 30 = 70
2100 ÷ 35 = 60
2100 ÷ 42 = 50
Therefore, the factors of 2100 are: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 2100 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2100 ÷ 2 = 1050
1050 ÷ 2 = 525
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 2100 are 2, 3, 5, and 7.
The prime factorization of 2100 is: 2² × 3 × 5² × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 2100 is divided by 2 to get 1050.
Step 2: Now divide 1050 by 2 to get 525.
Step 3: Then divide 525 by 3 to get 175.
Step 4: Divide 175 by 5 to get 35.
Step 5: Divide 35 by 5 to get 7.
Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 2100 is: 2² × 3 × 5² × 7.
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 2100: (1, 2100), (2, 1050), (3, 700), (4, 525), (5, 420), (6, 350), (7, 300), (10, 210), (12, 175), (14, 150), (15, 140), (20, 105), (21, 100), (25, 84), (28, 75), (30, 70), (35, 60), (42, 50).
Negative factor pairs of 2100: (-1, -2100), (-2, -1050), (-3, -700), (-4, -525), (-5, -420), (-6, -350), (-7, -300), (-10, -210), (-12, -175), (-14, -150), (-15, -140), (-20, -105), (-21, -100), (-25, -84), (-28, -75), (-30, -70), (-35, -60), (-42, -50).
Common Mistakes and How to Avoid Them in Factors of 2100
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 the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 2100, 1 and 2100 are also factors.
Factors of 2100 Examples
Problem 1
A company has 2100 pens and needs to distribute them equally among 14 departments. How many pens will each department receive?
Each department will receive 150 pens.
Explanation
To divide the pens equally, we need to divide the total pens by the number of departments.
2100/14 = 150
Problem 2
A rectangular garden has a total area of 2100 square meters with a length of 30 meters. What is the width of the garden?
The width is 70 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
2100 = 30 × width
To find the value of width, we need to shift 30 to the left side.
2100/30 = width
Width = 70.
Problem 3
There are 35 teams participating in a tournament, and each team has paid an entry fee that totals 2100. What was the entry fee per team?
The entry fee per team is 60.
Explanation
To find the entry fee per team, divide the total fee by the number of teams.
2100/35 = 60
Problem 4
A warehouse contains 2100 boxes and needs to be organized into 50 rows. How many boxes will each row contain?
Each row will contain 42 boxes.
Explanation
Dividing the total boxes by the number of rows gives the number of boxes in each row.
2100/50 = 42
Problem 5
A library plans to arrange 2100 books equally across 15 shelves. How many books will be placed on each shelf?
Each shelf will have 140 books.
Explanation
Divide total books by shelves.
2100/15 = 140
FAQs on Factors of 2100
1.What are the factors of 2100?
2.Mention the prime factors of 2100.
3.Is 2100 a multiple of 7?
4.Mention the factor pairs of 2100.
5.What is the square of 2100?
6.How can children in Australia use numbers in everyday life to understand Factors of 2100?
7.What are some fun ways kids in Australia can practice Factors of 2100 with numbers?
8.What role do numbers and Factors of 2100 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 2100 skills?
Important Glossaries for Factors of 2100
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, and 2100.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 2100.
- 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 2100 are (1, 2100), (2, 1050), etc.
- Prime factorization: The process of determining the prime numbers that multiply together to give the original number. For example, the prime factorization of 2100 is 2² × 3 × 5² × 7.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 2100 is a multiple of 7.
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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.
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