119 LearnersLast updated on May 26th, 2025
Factors of 3800
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 3800, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3800?
The numbers that divide 3800 evenly are known as factors of 3800.
A factor of 3800 is a number that divides the number without remainder.
The factors of 3800 are 1, 2, 4, 5, 8, 10, 19, 20, 25, 38, 40, 50, 76, 95, 100, 152, 190, 200, 380, 475, 760, 950, 1900, and 3800.
Negative factors of 3800: -1, -2, -4, -5, -8, -10, -19, -20, -25, -38, -40, -50, -76, -95, -100, -152, -190, -200, -380, -475, -760, -950, -1900, and -3800.
Prime factors of 3800: 2, 5, and 19.
Prime factorization of 3800: 2² × 5² × 19.
The sum of factors of 3800: 1 + 2 + 4 + 5 + 8 + 10 + 19 + 20 + 25 + 38 + 40 + 50 + 76 + 95 + 100 + 152 + 190 + 200 + 380 + 475 + 760 + 950 + 1900 + 3800 = 9370
How to Find Factors of 3800?
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 3800. Identifying the numbers which are multiplied to get the number 3800 is the multiplication method.
Step 1: Multiply 3800 by 1, 3800 × 1 = 3800.
Step 2: Check for other numbers that give 3800 after multiplying
2 × 1900 = 3800
4 × 950 = 3800
5 × 760 = 3800
8 × 475 = 3800
10 × 380 = 3800
19 × 200 = 3800
20 × 190 = 3800
25 × 152 = 3800
38 × 100 = 3800
40 × 95 = 3800
50 × 76 = 3800
Therefore, the positive factor pairs of 3800 are: (1, 3800), (2, 1900), (4, 950), (5, 760), (8, 475), (10, 380), (19, 200), (20, 190), (25, 152), (38, 100), (40, 95), and (50, 76). 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 3800 by 1, 3800 ÷ 1 = 3800.
Step 2: Continue dividing 3800 by the numbers until the remainder becomes 0.
3800 ÷ 1 = 3800
3800 ÷ 2 = 1900
3800 ÷ 4 = 950
3800 ÷ 5 = 760
3800 ÷ 8 = 475
3800 ÷ 10 = 380
3800 ÷ 19 = 200
3800 ÷ 20 = 190
3800 ÷ 25 = 152
3800 ÷ 38 = 100
3800 ÷ 40 = 95
3800 ÷ 50 = 76
Therefore, the factors of 3800 are: 1, 2, 4, 5, 8, 10, 19, 20, 25, 38, 40, 50, 76, 95, 100, 152, 190, 200, 380, 475, 760, 950, 1900, and 3800.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 3800 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3800 ÷ 2 = 1900
1900 ÷ 2 = 950
950 ÷ 5 = 190
190 ÷ 5 = 38
38 ÷ 19 = 2
2 ÷ 2 = 1
The prime factors of 3800 are 2, 5, and 19.
The prime factorization of 3800 is: 2² × 5² × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3800 is divided by 2 to get 1900.
Step 2: Now divide 1900 by 2 to get 950.
Step 3: Then divide 950 by 5 to get 190.
Step 4: Divide 190 by 5 to get 38.
Step 5: Finally, divide 38 by 19 to get 2, and then divide 2 by 2 to get 1. Here, 1 is the smallest number, indicating the end of the factor tree. So, the prime factorization of 3800 is: 2² × 5² × 19.
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 3800: (1, 3800), (2, 1900), (4, 950), (5, 760), (8, 475), (10, 380), (19, 200), (20, 190), (25, 152), (38, 100), (40, 95), and (50, 76).
Negative factor pairs of 3800: (-1, -3800), (-2, -1900), (-4, -950), (-5, -760), (-8, -475), (-10, -380), (-19, -200), (-20, -190), (-25, -152), (-38, -100), (-40, -95), and (-50, -76).
Common Mistakes and How to Avoid Them in Factors of 3800
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 3800, 1 and 3800 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 3800 consist of -1, -2, -4, 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 3800/1.5 = 2533.333, 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 3800 are prime numbers.
For example, 2, 5, and 19 are the prime factors of 3800, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3800 as 2² × 5² × 19 and missing all the key factors.
Factors of 3800 Examples
Problem 1
There are 20 boxes and 3800 candies. How will they distribute them equally?
They will get 190 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of boxes.
3800/20 = 190
Problem 2
A swimming pool is rectangular, the length of the pool is 95 meters and the total area is 3800 square meters. Find the width?
40 meters.
Explanation
To find the width of the pool, we use the formula,
Area = length × width
3800 = 95 × width
To find the value of width, we need to shift 95 to the left side.
3800/95 = width
Width = 40.
Problem 3
There are 76 shelves and 3800 books. How many books will be on each shelf?
Each shelf will have 50 books.
Explanation
To find the books on each shelf, divide the total books by the number of shelves.
3800/76 = 50
Problem 4
In a company, there are 3800 employees, and 190 teams. How many employees are there in each team?
There are 20 employees in each team.
Explanation
Dividing the employees by the total teams, we will get the number of employees in each team.
3800/190 = 20
Problem 5
3800 seeds need to be planted in 475 pots. How many seeds will go in each pot?
Each of the pots has 8 seeds.
Explanation
Divide total seeds by the number of pots.
3800/475 = 8
FAQs on Factors of 3800
1.What are the factors of 3800?
2.Mention the prime factors of 3800.
3.Is 3800 a multiple of 5?
4.Mention the factor pairs of 3800?
5.What is the square of 3800?
6.How can children in United States use numbers in everyday life to understand Factors of 3800?
7.What are some fun ways kids in United States can practice Factors of 3800 with numbers?
8.What role do numbers and Factors of 3800 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 3800 skills?
Important Glossaries for Factors of 3800
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3800 are 1, 2, 4, 5, 8, 10, 19, 20, 25, 38, 40, 50, 76, 95, 100, 152, 190, 200, 380, 475, 760, 950, 1900, and 3800.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 19 are prime factors of 3800.
- 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 3800 are (1, 3800), (2, 1900), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 3800 is 2² × 5² × 19.
- Division method: A method to find factors by dividing the number by whole numbers until the remainder is zero. For example, using this method to find factors of 3800.
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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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