Last updated on May 26th, 2025
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.
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.
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
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.
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.
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To divide the boxes equally, we need to divide the total boxes with the number of trucks. 25200/12 = 2100
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.
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.
There are 84 storage units and 25200 items. How many items will be in each storage unit?
Each storage unit will have 300 items.
To find the items in each storage unit, divide the total items by the number of units. 25200/84 = 300
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.
Dividing the students by the total classes, we will get the number of students in each class. 25200/120 = 210
25200 books need to be arranged in 420 shelves. How many books will go on each shelf?
Each of the shelves has 60 books.
Divide total books by shelves. 25200/420 = 60
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.
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.
: She loves to read number jokes and games.