118 LearnersLast updated on May 26th, 2025
Factors of 1800
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 1800, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1800?
The numbers that divide 1800 evenly are known as factors of 1800.
A factor of 1800 is a number that divides the number without remainder.
The factors of 1800 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, 300, 450, 600, 900, and 1800.
Negative factors of 1800: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -150, -180, -225, -300, -450, -600, -900, and -1800.
Prime factors of 1800: 2, 3, and 5.
Prime factorization of 1800: 2³ × 3² × 5².
The sum of factors of 1800: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 60 + 75 + 90 + 100 + 150 + 180 + 225 + 300 + 450 + 600 + 900 + 1800 = 5460
How to Find Factors of 1800?
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 1800. Identifying the numbers which are multiplied to get the number 1800 is the multiplication method.
Step 1: Multiply 1800 by 1, 1800 × 1 = 1800.
Step 2: Check for other numbers that give 1800 after multiplying
2 × 900 = 1800
3 × 600 = 1800
4 × 450 = 1800
5 × 360 = 1800
6 × 300 = 1800
9 × 200 = 1800
10 × 180 = 1800
12 × 150 = 1800
15 × 120 = 1800
18 × 100 = 1800
20 × 90 = 1800
25 × 72 = 1800
30 × 60 = 1800
36 × 50 = 1800
45 × 40 = 1800
Therefore, the positive factor pairs of 1800 are: (1, 1800), (2, 900), (3, 600), (4, 450), (5, 360), (6, 300), (9, 200), (10, 180), (12, 150), (15, 120), (18, 100), (20, 90), (25, 72), (30, 60), and (36, 50), (45, 40).
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 1800 by 1, 1800 ÷ 1 = 1800.
Step 2: Continue dividing 1800 by the numbers until the remainder becomes 0.
1800 ÷ 1 = 1800
1800 ÷ 2 = 900
1800 ÷ 3 = 600
1800 ÷ 4 = 450
1800 ÷ 5 = 360
1800 ÷ 6 = 300
1800 ÷ 9 = 200
1800 ÷ 10 = 180
1800 ÷ 12 = 150
1800 ÷ 15 = 120
1800 ÷ 18 = 100
1800 ÷ 20 = 90
1800 ÷ 25 = 72
1800 ÷ 30 = 60
1800 ÷ 36 = 50
1800 ÷ 45 = 40
Therefore, the factors of 1800 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 40, 45, 50, 60, 72, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 1800 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1800 ÷ 2 = 900
900 ÷ 2 = 450
450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 1800 are 2, 3, and 5.
The prime factorization of 1800 is: 2³ × 3² × 5².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1800 is divided by 2 to get 900.
Step 2: Now divide 900 by 2 to get 450.
Step 3: Then divide 450 by 2 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 1800 is: 2³ × 3² × 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 1800: (1, 1800), (2, 900), (3, 600), (4, 450), (5, 360), (6, 300), (9, 200), (10, 180), (12, 150), (15, 120), (18, 100), (20, 90), (25, 72), (30, 60), (36, 50), and (45, 40).
Negative factor pairs of 1800: (-1, -1800), (-2, -900), (-3, -600), (-4, -450), (-5, -360), (-6, -300), (-9, -200), (-10, -180), (-12, -150), (-15, -120), (-18, -100), (-20, -90), (-25, -72), (-30, -60), (-36, -50), and (-45, -40).
Common Mistakes and How to Avoid Them in Factors of 1800
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 1800, 1 and 1800 are also factors.
Factors of 1800 Examples
Problem 1
There are 18 guests and 1800 candies. How will they divide it equally?
They will get 100 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of guests.
1800/18 = 100
Problem 2
A garden is rectangular, the length of the garden is 45 meters and the total area is 1800 square meters. Find the width?
40 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1800 = 45 × width
To find the value of width, we need to shift 45 to the left side.
1800/45 = width
Width = 40.
Problem 3
There are 72 bags and 1800 marbles. How many marbles will be in each bag?
Each bag will have 25 marbles.
Explanation
To find the marbles in each bag, divide the total marbles with the bags.
1800/72 = 25
Problem 4
In a class, there are 1800 students, and 60 groups. How many students are there in each group?
There are 30 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1800/60 = 30
Problem 5
1800 books need to be arranged in 90 shelves. How many books will go on each shelf?
Each of the shelves has 20 books.
Explanation
Divide total books with shelves.
1800/90 = 20
FAQs on Factors of 1800
1.What are the factors of 1800?
2.Mention the prime factors of 1800.
3.Is 1800 a multiple of 12?
4.Mention the factor pairs of 1800?
5.What is the square of 1800?
6.How can children in Thailand use numbers in everyday life to understand Factors of 1800?
7.What are some fun ways kids in Thailand can practice Factors of 1800 with numbers?
8.What role do numbers and Factors of 1800 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 1800 skills?
Important Glossaries for Factor of 1800
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1800 are 1, 2, 3, 4, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 1800.
- 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 1800 are (1, 1800), (2, 900), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1800 is 2³ × 3² × 5².
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
Explore More numbers
Previous to Factors of 1800
About BrightChamps in Thailand
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.
