122 LearnersLast updated on May 26th, 2025
Factors of 1908
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 1908, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1908?
The numbers that divide 1908 evenly are known as factors of 1908.
A factor of 1908 is a number that divides the number without remainder.
The factors of 1908 are 1, 2, 3, 4, 6, 12, 13, 26, 27, 36, 39, 52, 54, 78, 108, 156, 169, 234, 312, 507, 676, 1014, and 1908.
Negative factors of 1908: -1, -2, -3, -4, -6, -12, -13, -26, -27, -36, -39, -52, -54, -78, -108, -156, -169, -234, -312, -507, -676, -1014, and -1908.
Prime factors of 1908: 2, 3, and 13.
Prime factorization of 1908: 2² × 3³ × 13.
The sum of factors of 1908: 1 + 2 + 3 + 4 + 6 + 12 + 13 + 26 + 27 + 36 + 39 + 52 + 54 + 78 + 108 + 156 + 169 + 234 + 312 + 507 + 676 + 1014 + 1908 = 5512
How to Find Factors of 1908?
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 1908. Identifying the numbers which are multiplied to get the number 1908 is the multiplication method.
Step 1: Multiply 1908 by 1, 1908 × 1 = 1908.
Step 2: Check for other numbers that give 1908 after multiplying:
2 × 954 = 1908
3 × 636 = 1908
4 × 477 = 1908
6 × 318 = 1908
12 × 159 = 1908
13 × 147 = 1908
18 × 106 = 1908
27 × 70.666... (not a factor pair)
54 × 35.333... (not a factor pair)
78 × 24.4615... (not a factor pair)
Thus, the positive factor pairs of 1908 include (1, 1908), (2, 954), (3, 636), (4, 477), (6, 318), (12, 159), (13, 147), and so on. 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 a simple division method:
Step 1: Divide 1908 by 1, 1908 ÷ 1 = 1908.
Step 2: Continue dividing 1908 by the numbers until the remainder becomes 0.
1908 ÷ 1 = 1908
1908 ÷ 2 = 954
1908 ÷ 3 = 636
1908 ÷ 4 = 477
1908 ÷ 6 = 318
1908 ÷ 12 = 159
1908 ÷ 13 = 147
Therefore, the factors of 1908 are 1, 2, 3, 4, 6, 12, 13, 26, 27, 36, 39, 52, 54, 78, 108, 156, 169, 234, 312, 507, 676, 1014, and 1908.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 1908 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
1908 ÷ 2 = 954
954 ÷ 2 = 477
477 ÷ 3 = 159
159 ÷ 3 = 53
53 ÷ 13 = 1
The prime factors of 1908 are 2, 3, and 13.
The prime factorization of 1908 is: 2² × 3³ × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 1908 is divided by 2 to get 954.
Step 2: Now divide 954 by 2 to get 477.
Step 3: Then divide 477 by 3 to get 159.
Step 4: Divide 159 by 3 to get 53.
Step 5: Finally, divide 53 by 13 to get 1. Here, 53 is the smallest prime number and cannot be divided further. So, the prime factorization of 1908 is: 2² × 3³ × 13.
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 1908: (1, 1908), (2, 954), (3, 636), (4, 477), (6, 318), (12, 159), (13, 147).
Negative factor pairs of 1908: (-1, -1908), (-2, -954), (-3, -636), (-4, -477), (-6, -318), (-12, -159), (-13, -147).
Common Mistakes and How to Avoid Them in Factors of 1908
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
People might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1908, 1 and 1908 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 1908 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Sometimes people might mistakenly add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 1908/1.5 ≈ 1272, which 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 1908 are prime numbers. In fact, 2, 3, and 13 are the prime factors of 1908, but it has other factors like 4, 6.
Mistake 5
Mistake in Factorization
Skipping steps in factorization can lead to writing incorrect factors.
For example, not breaking 1908 as 2² × 3³ × 13 and missing all key factors.
Factors of 1908 Examples
Problem 1
A company has 6 departments and 1908 employees. How will they distribute employees equally among departments?
Each department will have 318 employees.
Explanation
To distribute employees equally, divide the total employees by the number of departments.
1908/6 = 318
Problem 2
A garden is rectangular, the length of the garden is 13 meters, and the total area is 1908 square meters. Find the width?
Width is 147 meters.
Explanation
To find the width of the garden, use the formula, Area = length × width
1908 = 13 × width
To find the value of width, divide the area by the length.
1908/13 = width
Width = 147.
Problem 3
There are 12 classrooms and 1908 chairs. How many chairs will each classroom have?
Each classroom will have 159 chairs.
Explanation
To find the chairs in each classroom, divide the total chairs by the number of classrooms.
1908/12 = 159
Problem 4
A factory produces 1908 units, which need to be packed into 26 boxes. How many units will each box contain?
Each box will contain 73 units.
Explanation
Dividing the total units by the total boxes will give the number of units in each box.
1908/26 = 73
Problem 5
A library has 1908 books to be arranged on 54 shelves. How many books will go on each shelf?
Each shelf will have 35 books.
Explanation
Divide the total books by the number of shelves.
1908/54 = 35
FAQs on Factors of 1908
1.What are the factors of 1908?
2.Mention the prime factors of 1908.
3.Is 1908 a multiple of 4?
4.Mention the factor pairs of 1908?
5.What is the square of 1908?
6.How can children in Oman use numbers in everyday life to understand Factors of 1908?
7.What are some fun ways kids in Oman can practice Factors of 1908 with numbers?
8.What role do numbers and Factors of 1908 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve Factors of 1908 skills?
Important Glossaries for Factors of 1908
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1908 are 1, 2, 3, 4, 6, 12, 13, 26, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 1908.
- 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 1908 are (1, 1908), (2, 954), etc.
- Multiplication method: A method to find factors by identifying numbers that multiply to give the original number. For example, 6 × 318 = 1908.
- Division method: A method to find factors by dividing the original number by whole numbers to find divisors. For example, 1908 ÷ 6 = 318.
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About BrightChamps in Oman
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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