100 LearnersLast updated on May 26th, 2025
Factors of 13500
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 13500, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 13500?
The numbers that divide 13500 evenly are known as factors of 13500.
A factor of 13500 is a number that divides the number without remainder.
The factors of 13500 are 1, 2, 3, 4, 5, 6, 9, 10, 15, 18, 20, 25, 30, 36, 45, 50, 54, 75, 90, 100, 108, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 1800, 2700, 4500, 6750, and 13500.
Negative factors of 13500: -1, -2, -3, -4, -5, -6, -9, -10, -15, -18, -20, -25, -30, -36, -45, -50, -54, -75, -90, -100, -108, -150, -180, -225, -270, -300, -450, -540, -675, -900, -1350, -1800, -2700, -4500, -6750, and -13500.
Prime factors of 13500: 2, 3, and 5.
Prime factorization of 13500: 2² × 3³ × 5³.
The sum of factors of 13500: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 54 + 75 + 90 + 100 + 108 + 150 + 180 + 225 + 270 + 300 + 450 + 540 + 675 + 900 + 1350 + 1800 + 2700 + 4500 + 6750 + 13500 = 37908
How to Find Factors of 13500?
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 13500. Identifying the numbers which are multiplied to get the number 13500 is the multiplication method.
Step 1: Multiply 13500 by 1, 13500 × 1 = 13500.
Step 2: Check for other numbers that give 13500 after multiplying
2 × 6750 = 13500
3 × 4500 = 13500
5 × 2700 = 13500
6 × 2250 = 13500
9 × 1500 = 13500
10 × 1350 = 13500
15 × 900 = 13500
18 × 750 = 13500
20 × 675 = 13500
25 × 540 = 13500
30 × 450 = 13500
36 × 375 = 13500
45 × 300 = 13500
50 × 270 = 13500
54 × 250 = 13500
75 × 180 = 13500
90 × 150 = 13500
100 × 135 = 13500
108 × 125 = 13500
Therefore, the positive factor pairs of 13500 are: (1, 13500), (2, 6750), (3, 4500), (5, 2700), (6, 2250), (9, 1500), (10, 1350), (15, 900), (18, 750), (20, 675), (25, 540), (30, 450), (36, 375), (45, 300), (50, 270), (54, 250), (75, 180), (90, 150), (100, 135), (108, 125).
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 13500 by 1, 13500 ÷ 1 = 13500.
Step 2: Continue dividing 13500 by the numbers until the remainder becomes 0.
13500 ÷ 1 = 13500
13500 ÷ 2 = 6750
13500 ÷ 3 = 4500
13500 ÷ 5 = 2700
13500 ÷ 6 = 2250
13500 ÷ 9 = 1500
13500 ÷ 10 = 1350
13500 ÷ 15 = 900
13500 ÷ 18 = 750
13500 ÷ 20 = 675
13500 ÷ 25 = 540
13500 ÷ 30 = 450
13500 ÷ 36 = 375
13500 ÷ 45 = 300
13500 ÷ 50 = 270
13500 ÷ 54 = 250
13500 ÷ 75 = 180
13500 ÷ 90 = 150
13500 ÷ 100 = 135
13500 ÷ 108 = 125
Therefore, the factors of 13500 are: 1, 2, 3, 4, 5, 6, 9, 10, 15, 18, 20, 25, 30, 36, 45, 50, 54, 75, 90, 100, 108, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 1800, 2700, 4500, 6750, and 13500.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 13500 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
13500 ÷ 2 = 6750
6750 ÷ 2 = 3375
3375 ÷ 3 = 1125
1125 ÷ 3 = 375
375 ÷ 3 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 13500 are 2, 3, and 5.
The prime factorization of 13500 is: 2² × 3³ × 5³.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 13500 is divided by 2 to get 6750.
Step 2: Now divide 6750 by 2 to get 3375.
Step 3: Then divide 3375 by 3 to get 1125.
Step 4: Divide 1125 by 3 to get 375.
Step 5: Divide 375 by 3 to get 125.
Step 6: Divide 125 by 5 to get 25.
Step 7: Divide 25 by 5 to get 5.
Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 13500 is: 2² × 3³ × 5³.
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 13500: (1, 13500), (2, 6750), (3, 4500), (5, 2700), (6, 2250), (9, 1500), (10, 1350), (15, 900), (18, 750), (20, 675), (25, 540), (30, 450), (36, 375), (45, 300), (50, 270), (54, 250), (75, 180), (90, 150), (100, 135), (108, 125).
Negative factor pairs of 13500: (-1, -13500), (-2, -6750), (-3, -4500), (-5, -2700), (-6, -2250), (-9, -1500), (-10, -1350), (-15, -900), (-18, -750), (-20, -675), (-25, -540), (-30, -450), (-36, -375), (-45, -300), (-50, -270), (-54, -250), (-75, -180), (-90, -150), (-100, -135), (-108, -125).
Common Mistakes and How to Avoid Them in Factors of 13500
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 13500, 1 and 13500 are also factors.
Factors of 13500 Examples
Problem 1
There are 135 friends and 13500 stickers. How will they divide them equally?
They will get 100 stickers each.
Explanation
To divide the stickers equally, we need to divide the total stickers by the number of friends.
13500/135 = 100
Problem 2
A rectangular plot has a length of 300 meters and a total area of 13500 square meters. Find the width.
45 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
13500 = 300 × width
To find the value of width, we need to shift 300 to the left side.
13500/300 = width
Width = 45.
Problem 3
A baker has 6750 cupcakes and needs to pack them into 450 boxes. How many cupcakes will be in each box?
Each box will have 15 cupcakes.
Explanation
To find the cupcakes in each box, divide the total cupcakes by the boxes.
6750/450 = 15
Problem 4
In a school, there are 5400 students and 36 sections. How many students are there in each section?
There are 150 students in each section.
Explanation
Dividing the students by the total sections, we will get the number of students in each section.
5400/36 = 150
Problem 5
13500 books need to be arranged in 90 shelves. How many books will go on each shelf?
Each of the shelves has 150 books.
Explanation
Divide total books by shelves.
13500/90 = 150
FAQs on Factors of 13500
1.What are the factors of 13500?
2.Mention the prime factors of 13500.
3.Is 13500 a multiple of 5?
4.Mention the factor pairs of 13500?
5.What is the square of 13500?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 13500?
7.What are some fun ways kids in Bahrain can practice Factors of 13500 with numbers?
8.What role do numbers and Factors of 13500 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 13500 skills?
Important Glossaries for Factors of 13500
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 13500 are 1, 2, 3, 4, 5, 6, 9, 10, 15, 18, 20, 25, 30, 36, 45, 50, 54, 75, 90, 100, 108, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 1800, 2700, 4500, 6750, and 13500.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 13500.
- 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 13500 are (1, 13500), (2, 6750), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 13500 is 2² × 3³ × 5³.
- Divisors: Another term for factors, which are numbers dividing the given number without leaving a remainder. For example, the divisors of 13500 include 1, 2, 3, 4, 5, etc.
Explore More numbers
Previous to Factors of 13500
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.
