124 LearnersLast updated on May 26th, 2025
Factors of 25200
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 25200, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 25200?
The numbers that divide 25200 evenly are known as factors of 25200.
A factor of 25200 is a number that divides the number without remainder.
The factors of 25200 are numerous, including 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 48, 50, 56, 60, 63, 70, 72, 75, 80, 84, 90, 100, 105, 112, 120, 126, 140, 144, 150, 168, 175, 180, 200, 210, 225, 240, 252, 280, 300, 315, 336, 350, 360, 400, 420, 450, 504, 525, 560, 600, 630, 700, 720, 750, 840, 900, 1008, 1050, 1120, 1260, 1400, 1440, 1500, 1680, 1800, 2100, 2520, 2800, 3150, 3600, 4200, 5040, 6300, 8400, 12600, and 25200. Negative factors of 25200: -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -12, -14, -15, -16, -18, -20, -21, -24, -25, -28, -30, -35, -36, -40, -42, -45, -48, -50, -56, -60, -63, -70, -72, -75, -80, -84, -90, -100, -105, -112, -120, -126, -140, -144, -150, -168, -175, -180, -200, -210, -225, -240, -252, -280, -300, -315, -336, -350, -360, -400, -420, -450, -504, -525, -560, -600, -630, -700, -720, -750, -840, -900, -1008, -1050, -1120, -1260, -1400, -1440, -1500, -1680, -1800, -2100, -2520, -2800, -3150, -3600, -4200, -5040, -6300, -8400, -12600, -25
Prime factors of 25200: 2, 3, 5, and 7.
Prime factorization of 25200: 24 × 32 × 52 × 7.
How to Find Factors of 25200?
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 25200. Identifying the numbers which are multiplied to get the number 25200 is the multiplication method.
Step 1: Multiply 25200 by 1, 25200 × 1 = 25200.
Step 2: Check for other numbers that give 25200 after multiplying
2 × 12600 = 25200
3 × 8400 = 25200
4 × 6300 = 25200
5 × 5040 = 25200
6 × 4200 = 25200 ...
Therefore, the positive factor pairs of 25200 include: (1, 25200), (2, 12600), (3, 8400), (4, 6300), (5, 5040), (6, 4200), and many more. 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 25200 by 1, 25200 ÷ 1 = 25200.
Step 2: Continue dividing 25200 by the numbers until the remainder becomes 0.
25200 ÷ 1 = 25200
25200 ÷ 2 = 12600
25200 ÷ 3 = 8400
25200 ÷ 4 = 6300
25200 ÷ 5 = 5040
25200 ÷ 6 = 4200 ...
Therefore, the factors of 25200 include: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, and many more.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 25200 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
25200 ÷ 2 = 12600
12600 ÷ 2 = 6300
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 25200 are 2, 3, 5, and 7.
The prime factorization of 25200 is: 24 × 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, 25200 is divided by 2 to get 12600.
Step 2: Now divide 12600 by 2 to get 6300.
Step 3: Then divide 6300 by 2 to get 3150.
Step 4: Divide 3150 by 2 to get 1575.
Step 5: Divide 1575 by 3 to get 525.
Step 6: Divide 525 by 3 to get 175.
Step 7: Divide 175 by 5 to get 35. Step 8: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 25200 is: 2^4 × 3^2 × 5^2 × 7.
Common Mistakes and How to Avoid Them in Factors of 25200
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 25200, 1 and 25200 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 25200 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 25200/1.5 = 16800, and it 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 25200 are prime numbers. For example, 2, 3, 5, and 7 are the prime factors of 25200, but it has other factors like 4, 6, 8.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 25200 as 2^4 × 3^2 × 5^2 × 7 and missing all the key factors.
Factors of 25200 Examples
Problem 1
A warehouse has 25200 boxes and needs to be divided among 12 trucks equally. How many boxes will each truck carry?
Each truck will carry 2100 boxes.
Explanation
To divide the boxes equally, we need to divide the total boxes with the number of trucks. 25200/12 = 2100
Problem 2
A field is rectangular, the length of the field is 70 meters and the total area is 25200 square meters. Find the width?
360 meters.
Explanation
To find the width of the field, we use the formula, Area = length × width 25200 = 70 × width To find the value of width, we need to shift 70 to the left side. 25200/70 = width Width = 360.
Problem 3
There are 84 storage units and 25200 items. How many items will be in each storage unit?
Each storage unit will have 300 items.
Explanation
To find the items in each storage unit, divide the total items by the number of units. 25200/84 = 300
Problem 4
In a school, there are 25200 students, and 120 classes. How many students are there in each class?
There are 210 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class. 25200/120 = 210
Problem 5
25200 books need to be arranged in 420 shelves. How many books will go on each shelf?
Each of the shelves has 60 books.
Explanation
Divide total books by shelves. 25200/420 = 60
FAQs on Factors of 25200
1.What are the factors of 25200?
2.Mention the prime factors of 25200.
3.Is 25200 a multiple of 4?
4.Mention the factor pairs of 25200?
5.What is the square of 25200?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 25200?
7.What are some fun ways kids in Vietnam can practice Factors of 25200 with numbers?
8.What role do numbers and Factors of 25200 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 25200 skills?
Important Glossaries for Factors of 25200
Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 25200 include 1, 2, 3, 4, and many more.
Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 25200.
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 25200 include (1, 25200), (2, 12600), etc.
Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 25200 is 24 × 32 × 52 × 7.
Multiples: The result of multiplying a number by an integer. For example, 25200 is a multiple of 4.
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About BrightChamps in Vietnam
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
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