Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 19 teams and 1900 medals. How will they divide it equally?
They will get 100 medals each.
To divide the medals equally, we need to divide the total medals with the number of teams.
1900/19 = 100
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.
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.
There are 50 boxes and 1900 apples. How many apples will be in each box?
Each box will have 38 apples.
To find the apples in each box, divide the total apples with the boxes.
1900/50 = 38
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.
Dividing the employees with the total departments, we will get the number of employees in each department.
1900/95 = 20
1900 chairs need to be arranged in 100 rows. How many chairs will go in each row?
Each row has 19 chairs.
Divide total chairs with rows.
1900/100 = 19
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.
: She loves to read number jokes and games.