116 LearnersLast updated on June 2nd, 2025
Factors of 4050
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 4050, how they are used in real life, and tips to learn them quickly.
What are the Factors of 4050?
The numbers that divide 4050 evenly are known as factors of 4050.
A factor of 4050 is a number that divides the number without remainder.
The factors of 4050 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 81, 90, 135, 150, 162, 225, 270, 405, 450, 675, 810, 1350, 2025, and 4050.
Negative factors of 4050: -1, -2, -3, -5, -6, -9, -10, -15, -18, -25, -27, -30, -45, -50, -54, -75, -81, -90, -135, -150, -162, -225, -270, -405, -450, -675, -810, -1350, -2025, and -4050.
Prime factors of 4050: 2, 3, 5.
Prime factorization of 4050: 2 × 34 × 52.
The sum of factors of 4050: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 25 + 27 + 30 + 45 + 50 + 54 + 75 + 81 + 90 + 135 + 150 + 162 + 225 + 270 + 405 + 450 + 675 + 810 + 1350 + 2025 + 4050 = 10584.
How to Find Factors of 4050?
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 4050. Identifying the numbers which are multiplied to get the number 4050 is the multiplication method.
Step 1: Multiply 4050 by 1, 4050 × 1 = 4050.
Step 2: Check for other numbers that give 4050 after multiplying:
2 × 2025 = 4050
3 × 1350 = 4050
5 × 810 = 4050 and so on.
Therefore, the positive factor pairs of 4050 are: (1, 4050), (2, 2025), (3, 1350), (5, 810), etc. All these factor pairs result in 4050.
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 that result in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 4050 by 1, 4050 ÷ 1 = 4050.
Step 2: Continue dividing 4050 by the numbers until the remainder becomes 0.
4050 ÷ 1 = 4050
4050 ÷ 2 = 2025
4050 ÷ 3 = 1350
4050 ÷ 5 = 810 and so on.
Therefore, the factors of 4050 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 81, 90, 135, 150, 162, 225, 270, 405, 450, 675, 810, 1350, 2025, 4050.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 4050 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
4050 ÷ 2 = 2025
2025 ÷ 3 = 675
675 ÷ 3 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 4050 are 2, 3, and 5.
The prime factorization of 4050 is: 2 × 34 × 52.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 4050 is divided by 2 to get 2025.
Step 2: Now divide 2025 by 3 to get 675.
Step 3: Then divide 675 by 3 to get 225.
Step 4: Divide 225 by 3 to get 75.
Step 5: Divide 75 by 3 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 4050 is: 2 × 34 × 52.
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 4050: (1, 4050), (2, 2025), (3, 1350), (5, 810), etc.
Negative factor pairs of 4050: (-1, -4050), (-2, -2025), (-3, -1350), (-5, -810), etc.
Common Mistakes and How to Avoid Them in Factors of 4050
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 4050, 1 and 4050 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 4050 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 4050/1.5 = 2700, 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 4050 are prime numbers. For example, 2, 3, and 5 are the prime factors of 4050, but it has other factors like 6, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not correctly performing the factorization of 4050 as 2 × 34 × 52 and missing all the key factors.
Factors of 4050 Examples
Problem 1
A baker has 4050 cookies and needs to package them in boxes. If each box holds 27 cookies, how many boxes are needed?
150 boxes are needed.
Explanation
To find the number of boxes needed, divide the total cookies by the number of cookies per box.
4050/27 = 150
Problem 2
A rectangular garden has a perimeter of 4050 meters. If the length of the garden is 1350 meters, what is the width?
825 meters.
Explanation
To find the width of the garden, use the formula for perimeter:
Perimeter = 2 × (length + width)
4050 = 2 × (1350 + width)
2025 = 1350 + width
Width = 2025 - 1350
Width = 675.
Problem 3
A teacher has 4050 sheets of paper and wants to distribute them among 90 students. How many sheets does each student receive?
Each student receives 45 sheets.
Explanation
To find the number of sheets per student, divide the total sheets by the number of students.
4050/90 = 45
Problem 4
A community center has 4050 chairs that need to be arranged in 5 equal rows. How many chairs will be in each row?
Each row will have 810 chairs.
Explanation
Dividing the chairs by the total rows will yield the number of chairs in each row.
4050/5 = 810
Problem 5
There are 4050 tickets to be equally distributed among 50 volunteers. How many tickets will each volunteer receive?
Each volunteer will receive 81 tickets.
Explanation
Divide total tickets by the number of volunteers.
4050/50 = 81
FAQs on Factors of 4050
1.What are the factors of 4050?
2.Mention the prime factors of 4050.
3.Is 4050 a multiple of 9?
4.Mention the factor pairs of 4050?
5.What is the square of 4050?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 4050?
7.What are some fun ways kids in United Kingdom can practice Factors of 4050 with numbers?
8.What role do numbers and Factors of 4050 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 4050 skills?
Important Glossaries for Factors of 4050
- Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 4050 are 1, 2, 3, 5, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 4050.
- 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 4050 are (1, 4050), (2, 2025), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors, such as 2 × 34 × 52 for 4050.
- Multiplication method: A method used to find factors 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.
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