103 LearnersLast updated on May 26th, 2025
Factors of 1944
Factors are numbers that divide a given number evenly without a 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 1944, their applications in real life, and tips to learn them quickly.
What are the Factors of 1944?
The numbers that divide 1944 evenly are known as factors of 1944.
A factor of 1944 is a number that divides the number without remainder.
The factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, and 1944.
Negative factors of 1944: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -81, -108, -162, -216, -243, -324, -486, -648, -972, and -1944.
Prime factors of 1944: 2 and 3.
Prime factorization of 1944: 23 × 35.
The sum of factors of 1944: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 81 + 108 + 162 + 216 + 243 + 324 + 486 + 648 + 972 + 1944 = 5711.
How to Find Factors of 1944?
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 1944. Identifying the numbers which are multiplied to get the number 1944 is the multiplication method.
Step 1: Multiply 1944 by 1, 1944 × 1 = 1944.
Step 2: Check for other numbers that give 1944 after multiplying:
2 × 972 = 1944
3 × 648 = 1944
4 × 486 = 1944
6 × 324 = 1944
8 × 243 = 1944
9 × 216 = 1944
12 × 162 = 1944
18 × 108 = 1944
24 × 81 = 1944
27 × 72 = 1944
36 × 54 = 1944
Therefore, the positive factor pairs of 1944 are: (1, 1944), (2, 972), (3, 648), (4, 486), (6, 324), (8, 243), (9, 216), (12, 162), (18, 108), (24, 81), (27, 72), (36, 54).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 the simple division method
Step 1: Divide 1944 by 1, 1944 ÷ 1 = 1944.
Step 2: Continue dividing 1944 by the numbers until the remainder becomes 0.
1944 ÷ 1 = 1944
1944 ÷ 2 = 972
1944 ÷ 3 = 648
1944 ÷ 4 = 486
1944 ÷ 6 = 324
1944 ÷ 8 = 243
1944 ÷ 9 = 216
1944 ÷ 12 = 162
1944 ÷ 18 = 108
1944 ÷ 24 = 81
1944 ÷ 27 = 72
1944 ÷ 36 = 54
Therefore, the factors of 1944 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944.
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 1944 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1944 ÷ 2 = 972
972 ÷ 2 = 486
486 ÷ 2 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 1944 are 2 and 3.
The prime factorization of 1944 is: 23 × 35.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1944 is divided by 2 to get 972.
Step 2: Now divide 972 by 2 to get 486.
Step 3: Then divide 486 by 2 to get 243.
Step 4: Divide 243 by 3 to get 81.
Step 5: Divide 81 by 3 to get 27.
Step 6: Divide 27 by 3 to get 9.
Step 7: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1944 is: 23 × 35.
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 1944: (1, 1944), (2, 972), (3, 648), (4, 486), (6, 324), (8, 243), (9, 216), (12, 162), (18, 108), (24, 81), (27, 72), (36, 54).
Negative factor pairs of 1944: (-1, -1944), (-2, -972), (-3, -648), (-4, -486), (-6, -324), (-8, -243), (-9, -216), (-12, -162), (-18, -108), (-24, -81), (-27, -72), (-36, -54).
Common Mistakes and How to Avoid Them in Factors of 1944
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 1944, 1 and 1944 are also factors.
Factors of 1944 Examples
Problem 1
A baker needs to arrange 1944 pastries equally into boxes. If each box can hold 9 pastries, how many boxes are needed?
216 boxes are needed.
Explanation
To find the number of boxes needed, we divide the total pastries by the number of pastries per box.
1944/9 = 216
Problem 2
A rectangular garden has a length of 36 meters and an area of 1944 square meters. What is the width of the garden?
54 meters.
Explanation
To find the width of the garden, we use the formula:
Area = length × width
1944 = 36 × width
To find the value of width, we need to shift 36 to the other side.
1944/36 = width
Width = 54.
Problem 3
A school has organized a competition and has 1944 ribbons. If each participant gets 18 ribbons, how many participants are there?
There are 108 participants.
Explanation
To find the number of participants, divide the total ribbons by the ribbons each participant receives.
1944/18 = 108
Problem 4
A library has 1944 books to be arranged on 27 shelves. How many books will be on each shelf?
Each shelf will have 72 books.
Explanation
Dividing the total books by the number of shelves gives us the number of books per shelf.
1944/27 = 72
Problem 5
A concert hall has 1944 seats arranged equally in 81 rows. How many seats are there in each row?
Each row has 24 seats.
Explanation
Divide the total number of seats by the number of rows to find the seats per row.
1944/81 = 24
FAQs on Factors of 1944
1.What are the factors of 1944?
2.Mention the prime factors of 1944.
3.Is 1944 a multiple of 9?
4.Mention the factor pairs of 1944?
5.What is the square of 1944?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 1944?
7.What are some fun ways kids in United Kingdom can practice Factors of 1944 with numbers?
8.What role do numbers and Factors of 1944 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 1944 skills?
Important Glossaries for Factors of 1944
- Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1944 are 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 1944.
- 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 1944 are (1, 1944), (2, 972), etc.
- Prime factorization: Writing a number as a product of its prime factors. For example, 1944 = 23 × 35.
- Multiples: Numbers that can be divided by another number without leaving a remainder. For example, 1944 is a multiple of 9.
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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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