100 LearnersLast updated on May 26th, 2025
Factors of 1824
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 1824, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1824?
The numbers that divide 1824 evenly are known as factors of 1824.
A factor of 1824 is a number that divides the number without remainder.
The factors of 1824 are 1, 2, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, and 1824.
Negative factors of 1824: -1, -2, -4, -6, -8, -12, -16, -19, -24, -32, -38, -48, -57, -76, -96, -114, -152, -228, -304, -456, -608, -912, and -1824.
Prime factors of 1824: 2 and 19.
Prime factorization of 1824: 26 × 19.
The sum of factors of 1824: 1 + 2 + 4 + 6 + 8 + 12 + 16 + 19 + 24 + 32 + 38 + 48 + 57 + 76 + 96 + 114 + 152 + 228 + 304 + 456 + 608 + 912 + 1824 = 4968
How to Find Factors of 1824?
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 1824. Identifying the numbers which are multiplied to get the number 1824 is the multiplication method.
Step 1: Multiply 1824 by 1, 1824 × 1 = 1824.
Step 2: Check for other numbers that give 1824 after multiplying
2 × 912 = 1824
4 × 456 = 1824
6 × 304 = 1824
8 × 228 = 1824
12 × 152 = 1824
16 × 114 = 1824
19 × 96 = 1824
24 × 76 = 1824
32 × 57 = 1824
38 × 48 = 1824
Therefore, the positive factor pairs of 1824 are: (1, 1824), (2, 912), (4, 456), (6, 304), (8, 228), (12, 152), (16, 114), (19, 96), (24, 76), (32, 57), (38, 48).
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 1824 by 1, 1824 ÷ 1 = 1824.
Step 2: Continue dividing 1824 by the numbers until the remainder becomes 0.
1824 ÷ 1 = 1824
1824 ÷ 2 = 912
1824 ÷ 4 = 456
1824 ÷ 6 = 304
1824 ÷ 8 = 228
1824 ÷ 12 = 152
1824 ÷ 16 = 114
1824 ÷ 19 = 96
1824 ÷ 24 = 76
1824 ÷ 32 = 57
1824 ÷ 38 = 48
Therefore, the factors of 1824 are: 1, 2, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, and 1824.
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 1824 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1824 ÷ 2 = 912
912 ÷ 2 = 456
456 ÷ 2 = 228
228 ÷ 2 = 114
114 ÷ 2 = 57
57 ÷ 19 = 3
3 ÷ 3 = 1
The prime factors of 1824 are 2 and 19.
The prime factorization of 1824 is: 2^6 × 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, 1824 is divided by 2 to get 912.
Step 2: Now divide 912 by 2 to get 456.
Step 3: Then divide 456 by 2 to get 228.
Step 4: Divide 228 by 2 to get 114.
Step 5: Divide 114 by 2 to get 57.
Step 6: Finally, divide 57 by 19 to get 3.
Here, 3 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1824 is: 2^6 × 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 1824: (1, 1824), (2, 912), (4, 456), (6, 304), (8, 228), (12, 152), (16, 114), (19, 96), (24, 76), (32, 57), (38, 48).
Negative factor pairs of 1824: (-1, -1824), (-2, -912), (-4, -456), (-6, -304), (-8, -228), (-12, -152), (-16, -114), (-19, -96), (-24, -76), (-32, -57), (-38, -48).
Common Mistakes and How to Avoid Them in Factors of 1824
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1824, 1 and 1824 are also factors.
Factors of 1824 Examples
Problem 1
There are 16 rooms in a hotel and 1824 guests. How will the guests be distributed equally?
Each room will host 114 guests.
Explanation
To distribute the guests equally, we need to divide the total guests by the number of rooms.
1824/16 = 114
Problem 2
A garden is rectangular, the length of the garden is 24 meters, and the total area is 1824 square meters. Find the width?
76 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1824 = 24 × width
To find the value of width, we need to shift 24 to the left side.
1824/24 = width
Width = 76.
Problem 3
There are 38 buses and 1824 passengers. How many passengers will be in each bus?
Each bus will have 48 passengers.
Explanation
To find the passengers in each bus, divide the total passengers by the number of buses.
1824/38 = 48
Problem 4
In a school, there are 912 students, and 2 sessions. How many students are there in each session?
There are 456 students in each session.
Explanation
Dividing the students by the total sessions, we will get the number of students in each session.
912/2 = 456
Problem 5
1824 books need to be arranged in 304 shelves. How many books will go on each shelf?
Each of the shelves has 6 books.
Explanation
Divide total books by shelves.
1824/304 = 6
FAQs on Factors of 1824
1.What are the factors of 1824?
2.Mention the prime factors of 1824.
3.Is 1824, a multiple of 32?
4.Mention the factor pairs of 1824?
5.What is the square of 1824?
6.How can children in Thailand use numbers in everyday life to understand Factors of 1824?
7.What are some fun ways kids in Thailand can practice Factors of 1824 with numbers?
8.What role do numbers and Factors of 1824 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 1824 skills?
Important Glossaries for Factor of 1824
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1824 are 1, 2, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, and 1824.
- Prime factors: The factors which are prime numbers. For example, 2 and 19 are prime factors of 1824.
- 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 1824 are (1, 1824), (2, 912), etc.
- Prime factorization: Breaking down a number into its prime components. For example, the prime factorization of 1824 is 2^6 × 19.
- Multiplication method: A way to find factors by identifying pairs of numbers multiplied to give the original number. For example, the multiplication method for 1824 includes (1, 1824), (2, 912), etc.
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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.
Fun Fact
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