101 LearnersLast updated on May 26th, 2025
Factors of 1140
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 1140, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1140?
The numbers that divide 1140 evenly are known as factors of 1140.
A factor of 1140 is a number that divides the number without remainder.
The factors of 1140 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, and 1140.
Negative factors of 1140: -1, -2, -3, -4, -5, -6, -10, -12, -15, -19, -20, -30, -38, -57, -60, -76, -95, -114, -190, -228, -285, -380, -570, -1140.
Prime factors of 1140: 2, 3, 5, and 19.
Prime factorization of 1140: 2² × 3 × 5 × 19.
The sum of factors of 1140: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 19 + 20 + 30 + 38 + 57 + 60 + 76 + 95 + 114 + 190 + 228 + 285 + 380 + 570 + 1140 = 3780
How to Find Factors of 1140?
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 1140. Identifying the numbers which are multiplied to get the number 1140 is the multiplication method.
Step 1: Multiply 1140 by 1, 1140 × 1 = 1140.
Step 2: Check for other numbers that give 1140 after multiplying
2 × 570 = 1140
3 × 380 = 1140
4 × 285 = 1140
5 × 228 = 1140
6 × 190 = 1140
10 × 114 = 1140
12 × 95 = 1140
15 × 76 = 1140
19 × 60 = 1140
30 × 38 = 1140
Therefore, the positive factor pairs of 1140 are: (1, 1140), (2, 570), (3, 380), (4, 285), (5, 228), (6, 190), (10, 114), (12, 95), (15, 76), (19, 60), (30, 38).
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 1140 by 1, 1140 ÷ 1 = 1140.
Step 2: Continue dividing 1140 by the numbers until the remainder becomes 0.
1140 ÷ 1 = 1140
1140 ÷ 2 = 570
1140 ÷ 3 = 380
1140 ÷ 4 = 285
1140 ÷ 5 = 228
1140 ÷ 6 = 190
1140 ÷ 10 = 114
1140 ÷ 12 = 95
1140 ÷ 15 = 76
1140 ÷ 19 = 60
1140 ÷ 30 = 38
Therefore, the factors of 1140 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, 1140.
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 1140 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1140 ÷ 2 = 570
570 ÷ 2 = 285
285 ÷ 3 = 95
95 ÷ 5 = 19
19 ÷ 19 = 1
The prime factors of 1140 are 2, 3, 5, and 19.
The prime factorization of 1140 is: 2² × 3 × 5 × 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, 1140 is divided by 2 to get 570.
Step 2: Now divide 570 by 2 to get 285.
Step 3: Then divide 285 by 3 to get 95.
Step 4: Divide 95 by 5 to get 19. Here, 19 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1140 is: 2² × 3 × 5 × 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 1140: (1, 1140), (2, 570), (3, 380), (4, 285), (5, 228), (6, 190), (10, 114), (12, 95), (15, 76), (19, 60), (30, 38).
Negative factor pairs of 1140: (-1, -1140), (-2, -570), (-3, -380), (-4, -285), (-5, -228), (-6, -190), (-10, -114), (-12, -95), (-15, -76), (-19, -60), (-30, -38).
Common Mistakes and How to Avoid Them in Factors of 1140
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 1140, 1 and 1140 are also factors.
Factors of 1140 Examples
Problem 1
There are 6 teams and 1140 marbles. How will they divide it equally?
They will get 190 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of teams.
1140/6 = 190
Problem 2
A rectangular plot has a width of 19 meters and a total area of 1140 square meters. Find the length?
60 meters.
Explanation
To find the length of the plot, we use the formula, Area = length × width 1140 = length × 19
To find the value of length, we need to shift 19 to the left side.
1140/19 = length
Length = 60.
Problem 3
There are 95 boxes and 1140 nails. How many nails will be in each box?
Each box will have 12 nails.
Explanation
To find the nails in each box, divide the total nails by the boxes.
1140/95 = 12
Problem 4
In a theater, there are 1140 seats and 38 rows. How many seats are there in each row?
There are 30 seats in each row.
Explanation
Dividing the seats by the total rows, we will get the number of seats in each row.
1140/38 = 30
Problem 5
1140 books need to be arranged in 15 shelves. How many books will go on each shelf?
Each of the shelves has 76 books.
Explanation
Divide total books by shelves.
1140/15 = 76
FAQs on Factors of 1140
1.What are the factors of 1140?
2.Mention the prime factors of 1140.
3.Is 1140 a multiple of 19?
4.Mention the factor pairs of 1140?
5.What is the square of 1140?
Important Glossaries for Factors of 1140
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1140 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, and 1140.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 19 are prime factors of 1140.
- 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 1140 are (1, 1140), (2, 570), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1140 is 2² × 3 × 5 × 19.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method to find factors of 1140 involves identifying pairs like (2, 570).
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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
: She loves to read number jokes and games.
