126 LearnersLast updated on May 26th, 2025
Factors of 1900
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 1900, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1900?
The numbers that divide 1900 evenly are known as factors of 1900. A factor of 1900 is a number that divides the number without remainder.
The factors of 1900 are 1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 380, 475, 950, and 1900.
Negative factors of 1900: -1, -2, -4, -5, -10, -19, -20, -25, -38, -50, -76, -95, -100, -190, -380, -475, -950, and -1900.
Prime factors of 1900: 2, 5, and 19.
Prime factorization of 1900: 2 × 2 × 5 × 5 × 19.
The sum of factors of 1900: 1 + 2 + 4 + 5 + 10 + 19 + 20 + 25 + 38 + 50 + 76 + 95 + 100 + 190 + 380 + 475 + 950 + 1900 = 4350
How to Find Factors of 1900?
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 1900. Identifying the numbers which are multiplied to get the number 1900 is the multiplication method.
Step 1: Multiply 1900 by 1, 1900 × 1 = 1900.
Step 2: Check for other numbers that give 1900 after multiplying
2 × 950 = 1900
4 × 475 = 1900
5 × 380 = 1900
10 × 190 = 1900
20 × 95 = 1900
25 × 76 = 1900
50 × 38 = 1900
Therefore, the positive factor pairs of 1900 are: (1, 1900), (2, 950), (4, 475), (5, 380), (10, 190), (20, 95), (25, 76), (50, 38). 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 1900 by 1, 1900 ÷ 1 = 1900.
Step 2: Continue dividing 1900 by the numbers until the remainder becomes 0.
1900 ÷ 1 = 1900
1900 ÷ 2 = 950
1900 ÷ 4 = 475
1900 ÷ 5 = 380
1900 ÷ 10 = 190
1900 ÷ 20 = 95
1900 ÷ 25 = 76
1900 ÷ 38 = 50
Therefore, the factors of 1900 are: 1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 380, 475, 950, 1900.
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 1900 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1900 ÷ 2 = 950
950 ÷ 2 = 475
475 ÷ 5 = 95
95 ÷ 5 = 19
19 ÷ 19 = 1
The prime factors of 1900 are 2, 5, and 19.
The prime factorization of 1900 is: 2 × 2 × 5 × 5 × 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, 1900 is divided by 2 to get 950.
Step 2: Now divide 950 by 2 to get 475.
Step 3: Then divide 475 by 5 to get 95.
Step 4: Divide 95 by 5 to get 19. Here, 19 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1900 is: 2 × 2 × 5 × 5 × 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 1900: (1, 1900), (2, 950), (4, 475), (5, 380), (10, 190), (20, 95), (25, 76), (50, 38).
Negative factor pairs of 1900: (-1, -1900), (-2, -950), (-4, -475), (-5, -380), (-10, -190), (-20, -95), (-25, -76), (-50, -38).
Common Mistakes and How to Avoid Them in Factors of 1900
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 1900, 1 and 1900 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 1900 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 1900/1.5 ≈ 1266.67, 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 1900 are prime numbers. For example, 2, 5, and 19 are the prime factors of 1900, but it has other factors like 4, 95.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1900 as 2 × 2 × 5 × 5 × 19 and missing all the key factors.
Factors of 1900 Examples
Problem 1
There are 19 teams and 1900 medals. How will they divide it equally?
They will get 100 medals each.
Explanation
To divide the medals equally, we need to divide the total medals with the number of teams.
1900/19 = 100
Problem 2
A garden is rectangular, the length of the garden is 25 meters and the total area is 1900 square meters. Find the width?
76 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
1900 = 25 × width
To find the value of width, we need to shift 25 to the left side.
1900/25 = width
Width = 76.
Problem 3
There are 50 boxes and 1900 apples. How many apples will be in each box?
Each box will have 38 apples.
Explanation
To find the apples in each box, divide the total apples with the boxes.
1900/50 = 38
Problem 4
In a company, there are 1900 employees and 95 departments. How many employees are there in each department?
There are 20 employees in each department.
Explanation
Dividing the employees with the total departments, we will get the number of employees in each department.
1900/95 = 20
Problem 5
1900 chairs need to be arranged in 100 rows. How many chairs will go in each row?
Each row has 19 chairs.
Explanation
Divide total chairs with rows.
1900/100 = 19
FAQs on Factors of 1900
1.What are the factors of 1900?
2.Mention the prime factors of 1900.
3.Is 1900 a multiple of 25?
4.Mention the factor pairs of 1900?
5.What is the square of 1900?
6.How can children in United States use numbers in everyday life to understand Factors of 1900?
7.What are some fun ways kids in United States can practice Factors of 1900 with numbers?
8.What role do numbers and Factors of 1900 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 1900 skills?
Important Glossaries for Factors of 1900
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1900 are 1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 380, 475, 950, and 1900.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 19 are prime factors of 1900.
- 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 1900 are (1, 1900), (2, 950), etc.
- Multiples: Numbers that are the product of a given number and an integer. For example, 1900 is a multiple of 10.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1900 is 2 × 2 × 5 × 5 × 19.
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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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