121 LearnersLast updated on May 26th, 2025
Factors of 4500
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 4500, how they are used in real life, and tips to learn them quickly.
What are the Factors of 4500?
The numbers that divide 4500 evenly are known as factors of 4500. A factor of 4500 is a number that divides the number without remainder. The factors of 4500 include 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 250, 300, 450, 500, 750, 900, 1500, 2250, and 4500. Negative factors of 4500: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -150, -180, -225, -250, -300, -450, -500, -750, -900, -1500, -2250, and -4500. Prime factors of 4500: 2, 3, and 5. Prime factorization of 4500: 2^2 × 3^2 × 5^3. The sum of factors of 4500: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 60 + 75 + 90 + 100 + 150 + 180 + 225 + 250 + 300 + 450 + 500 + 750 + 900 + 1500 + 2250 + 4500 = 12696.
How to Find Factors of 4500?
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 4500. Identifying the numbers which are multiplied to get the number 4500 is the multiplication method.
Step 1: Multiply 4500 by 1, 4500 × 1 = 4500.
Step 2: Check for other numbers that give 4500 after multiplying
2 × 2250 = 4500
3 × 1500 = 4500
5 × 900 = 4500
6 × 750 = 4500
9 × 500 = 4500
10 × 450 = 4500
12 × 375 = 4500
15 × 300 = 4500
18 × 250 = 4500
20 × 225 = 4500
25 × 180 = 4500
30 × 150 = 4500
36 × 125 = 4500
45 × 100 = 4500
50 × 90 = 4500
60 × 75 = 4500
Therefore, the positive factor pairs of 4500 are: (1, 4500), (2, 2250), (3, 1500), (5, 900), (6, 750), (9, 500), (10, 450), (12, 375), (15, 300), (18, 250), (20, 225), (25, 180), (30, 150), (36, 125), (45, 100), (50, 90), and (60, 75).
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 4500 by 1, 4500 ÷ 1 = 4500.
Step 2: Continue dividing 4500 by the numbers until the remainder becomes 0.
4500 ÷ 1 = 4500
4500 ÷ 2 = 2250
4500 ÷ 3 = 1500
4500 ÷ 5 = 900
4500 ÷ 6 = 750
4500 ÷ 9 = 500
4500 ÷ 10 = 450
4500 ÷ 12 = 375
4500 ÷ 15 = 300
4500 ÷ 18 = 250
4500 ÷ 20 = 225
4500 ÷ 25 = 180
4500 ÷ 30 = 150
4500 ÷ 36 = 125
4500 ÷ 45 = 100
4500 ÷ 50 = 90
4500 ÷ 60 = 75
Therefore, the factors of 4500 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 250, 300, 450, 500, 750, 900, 1500, 2250, and 4500.
Prime Factors and Prime Factorization
The factors can be found by dividing by 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 4500 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
4500 ÷ 2 = 2250
2250 ÷ 2 = 1125
1125 ÷ 3 = 375
375 ÷ 3 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 4500 are 2, 3, and 5.
The prime factorization of 4500 is: 22 × 32 × 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, 4500 is divided by 2 to get 2250.
Step 2: Now divide 2250 by 2 to get 1125.
Step 3: Then divide 1125 by 3 to get 375.
Step 4: Divide 375 by 3 to get 125.
Step 5: Divide 125 by 5 to get 25.
Step 6: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 4500 is: 22 × 32 × 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 4500: (1, 4500), (2, 2250), (3, 1500), (5, 900), (6, 750), (9, 500), (10, 450), (12, 375), (15, 300), (18, 250), (20, 225), (25, 180), (30, 150), (36, 125), (45, 100), (50, 90), and (60, 75).
Negative factor pairs of 4500: (-1, -4500), (-2, -2250), (-3, -1500), (-5, -900), (-6, -750), (-9, -500), (-10, -450), (-12, -375), (-15, -300), (-18, -250), (-20, -225), (-25, -180), (-30, -150), (-36, -125), (-45, -100), (-50, -90), and (-60, -75).
Common Mistakes and How to Avoid Them in Factors of 4500
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 4500, 1 and 4500 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 4500 include -1, -2, -3, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 is a factor is incorrect, because 4500/1.5 = 3000, and it is not an integer.
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 4500 are prime numbers. For example, 2, 3, and 5 are the prime factors of 4500, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 4500 as 22 × 32 × 53 and missing all the key factors.
Factors of 4500 Examples
Problem 1
There are 90 students and 4500 pencils. How will they divide them equally?
They will get 50 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils by the number of students.
4500/90 = 50
Problem 2
A plot is rectangular, the length of the plot is 50 meters, and the total area is 4500 square meters. Find the width?
90 meters.
Explanation
To find the width of the plot, we use the formula, Area = length × width
4500 = 50 × width
To find the value of width, we need to divide 4500 by 50.
4500/50 = width
Width = 90.
Problem 3
There are 75 gift bags and 4500 candies. How many candies will be in each bag?
Each bag will have 60 candies.
Explanation
To find the candies in each bag, divide the total candies by the number of bags.
4500/75 = 60
Problem 4
In a factory, there are 4500 pieces of equipment, and they need to be packed in 100 boxes. How many pieces will be there in each box?
There will be 45 pieces in each box.
Explanation
Dividing the equipment by the total boxes, we will get the number of pieces in each box.
4500/100 = 45
Problem 5
4500 chairs need to be arranged in 225 rows. How many chairs will go in each row?
Each row will have 20 chairs.
Explanation
Divide total chairs by rows.
4500/225 = 20
FAQs on Factors of 4500
1.What are the factors of 4500?
2.Mention the prime factors of 4500.
3.Is 4500 a multiple of 25?
4.Mention the factor pairs of 4500?
5.What is the square of 4500?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 4500?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 4500 with numbers?
8.What role do numbers and Factors of 4500 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 4500 skills?
Important Glossaries for Factor of 4500
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 4500 are 1, 2, 3, 4, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 4500.
- 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 4500 are (1, 4500), (2, 2250), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 4500 is 22 × 32 × 53.
- Multiples: A number that can be divided by another number without a remainder. For example, 4500 is a multiple of 25.
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About BrightChamps in United Arab Emirates
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.
