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 1908, how they are used in real life, and tips to learn them quickly.
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
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 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.
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.
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 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A company has 6 departments and 1908 employees. How will they distribute employees equally among departments?
Each department will have 318 employees.
To distribute employees equally, divide the total employees by the number of departments.
1908/6 = 318
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.
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.
There are 12 classrooms and 1908 chairs. How many chairs will each classroom have?
Each classroom will have 159 chairs.
To find the chairs in each classroom, divide the total chairs by the number of classrooms.
1908/12 = 159
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.
Dividing the total units by the total boxes will give the number of units in each box.
1908/26 = 73
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.
Divide the total books by the number of shelves.
1908/54 = 35
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.