118 LearnersLast updated on May 26th, 2025
Factors of 6300
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 6300, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 6300?
The numbers that divide 6300 evenly are known as factors of 6300.
A factor of 6300 is a number that divides the number without remainder.
The factors of 6300 include numbers like 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150, and 6300.
Negative factors of 6300: Corresponding negative values such as -1, -2, -3, -4, -5, -6, -7, -9, -10, -12, -14, -15, -18, -20, -21, -25, -28, -30, -35, -36, -42, -45, -50, -60, -63, -70, -75, -84, -90, -100, -105, -126, -140, -150, -175, -180, -210, -252, -300, -315, -350, -420, -450, -525, -630, -700, -900, -1050, -1260, -1575, -2100, -3150, and -6300.
Prime factors of 6300: 2, 3, 5, and 7.
Prime factorization of 6300: 2² × 3² × 5² × 7.
The sum of factors of 6300 is a larger number that can be calculated by adding all of the factors listed above.
How to Find Factors of 6300?
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 6300. Identifying the numbers which are multiplied to get the number 6300 is the multiplication method.
Step 1: Multiply 6300 by 1, 6300 × 1 = 6300.
Step 2: Check for other numbers that give 6300 after multiplying. Here are some examples:
2 × 3150 = 6300
3 × 2100 = 6300
5 × 1260 = 6300
6 × 1050 = 6300
7 × 900 = 6300
Therefore, the positive factor pairs of 6300 are: (1, 6300), (2, 3150), (3, 2100), (5, 1260), (6, 1050), (7, 900), and many more.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 the simple division method
Step 1: Divide 6300 by 1, 6300 ÷ 1 = 6300.
Step 2: Continue dividing 6300 by numbers until the remainder becomes 0. Examples include:
6300 ÷ 1 = 6300
6300 ÷ 2 = 3150
6300 ÷ 3 = 2100
6300 ÷ 5 = 1260
6300 ÷ 6 = 1050
6300 ÷ 7 = 900
Therefore, the factors of 6300 include: 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150, 6300.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 6300 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
6300 ÷ 2 = 3150
3150 ÷ 2 = 1575
1575 ÷ 3 = 525
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 6300 are 2, 3, 5, and 7.
The prime factorization of 6300 is: 2² × 3² × 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, 6300 is divided by 2 to get 3150.
Step 2: Now divide 3150 by 2 to get 1575.
Step 3: Then divide 1575 by 3 to get 525.
Step 4: Divide 525 by 3 to get 175.
Step 5: Divide 175 by 5 to get 35.
Step 6: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 6300 is: 2² × 3² × 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 6300 include: (1, 6300), (2, 3150), (3, 2100), (5, 1260), (6, 1050), (7, 900), etc.
Negative factor pairs of 6300 include: (-1, -6300), (-2, -3150), (-3, -2100), (-5, -1260), (-6, -1050), (-7, -900), etc.
Common Mistakes and How to Avoid Them in Factors of 6300
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 6300, 1 and 6300 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 6300 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor is incorrect because 6300/1.5 is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 6300 are prime numbers is incorrect. For instance, 2, 3, 5, and 7 are the prime factors of 6300, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 6300 as 2² × 3² × 5² × 7 and missing all the key factors.
Factors of 6300 Examples
Problem 1
A party planner needs to arrange 6300 chairs in equal rows for an event. If each row can have 90 chairs, how many rows will there be?
There will be 70 rows.
Explanation
To find the number of rows, divide the total number of chairs by the number of chairs per row.
6300/90 = 70
Problem 2
A warehouse has 6300 boxes to be packed into crates. If each crate can hold 150 boxes, how many crates are needed?
42 crates are needed.
Explanation
To determine the number of crates, divide the total boxes by the capacity of each crate.
6300/150 = 42
Problem 3
A company has 6300 tasks to be completed by 35 teams. How many tasks will each team handle?
Each team will handle 180 tasks.
Explanation
To find the tasks assigned to each team, divide the total tasks by the number of teams.
6300/35 = 180
Problem 4
A factory produces 6300 units of a product using 25 machines. How many units does each machine produce?
Each machine produces 252 units.
Explanation
Divide the total units by the number of machines to find the production per machine.
6300/25 = 252
Problem 5
6300 liters of water need to be distributed equally into 210 containers. How much water will each container hold?
Each container will hold 30 liters.
Explanation
Divide the total liters of water by the number of containers.
6300/210 = 30
FAQs on Factors of 6300
1.What are the factors of 6300?
2.Mention the prime factors of 6300.
3.Is 6300 a multiple of 5?
4.Mention the factor pairs of 6300?
5.What is the square of 6300?
6.How can children in United States use numbers in everyday life to understand Factors of 6300?
7.What are some fun ways kids in United States can practice Factors of 6300 with numbers?
8.What role do numbers and Factors of 6300 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 6300 skills?
Important Glossaries for Factor of 6300
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 6300 include 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 6300.
- 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 6300 include (1, 6300), (2, 3150), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 6300 is 2² × 3² × 5² × 7.
- Multiplication method: A method to find factor pairs by identifying pairs of numbers that multiply to give the original number.
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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.
Fun Fact
: She loves to read number jokes and games.
