106 LearnersLast updated on May 26th, 2025
Factors of 1146
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 1146, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1146?
The numbers that divide 1146 evenly are known as factors of 1146. A factor of 1146 is a number that divides the number without remainder. The factors of 1146 are 1, 2, 3, 6, 9, 18, 31, 62, 57, 93, 186, 381, 573, and 1146.
Negative factors of 1146: -1, -2, -3, -6, -9, -18, -31, -62, -57, -93, -186, -381, -573, and -1146.
Prime factors of 1146: 2, 3, and 191.
Prime factorization of 1146: 2 × 3 × 191.
The sum of factors of 1146: 1 + 2 + 3 + 6 + 9 + 18 + 31 + 62 + 57 + 93 + 186 + 381 + 573 + 1146 = 2568.
How to Find Factors of 1146?
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 1146. Identifying the numbers which are multiplied to get the number 1146 is the multiplication method.
Step 1: Multiply 1146 by 1, 1146 × 1 = 1146.
Step 2: Check for other numbers that give 1146 after multiplying
2 × 573 = 1146
3 × 382 = 1146
6 × 191 = 1146
9 × 127 = 1146
18 × 63.67 = 1146 (but 63.67 is not a whole number, so it's not a factor pair)
31 × 37 = 1146
Therefore, the positive factor pairs of 1146 are: (1, 1146), (2, 573), (3, 382), (6, 191), (9, 127), (31, 37). All these factor pairs result in 1146. 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 1146 by 1, 1146 ÷ 1 = 1146.
Step 2: Continue dividing 1146 by the numbers until the remainder becomes 0.
1146 ÷ 1 = 1146
1146 ÷ 2 = 573
1146 ÷ 3 = 382
1146 ÷ 6 = 191
1146 ÷ 9 = 127
1146 ÷ 31 = 37
Therefore, the factors of 1146 are: 1, 2, 3, 6, 9, 31, 37, 62, 114, 186, 381, 573, and 1146.
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 1146 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1146 ÷ 2 = 573
573 ÷ 3 = 191
191 is a prime number.
The prime factors of 1146 are 2, 3, and 191. The prime factorization of 1146 is: 2 × 3 × 191.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 1146 is divided by 2 to get 573.
Step 2: Now divide 573 by 3 to get 191.
Step 3: 191 is a prime number and cannot be divided further by any number other than 1 and itself. So, the prime factorization of 1146 is: 2 × 3 × 191.
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 1146: (1, 1146), (2, 573), (3, 382), (6, 191), (9, 127), and (31, 37).
- Negative factor pairs of 1146: (-1, -1146), (-2, -573), (-3, -382), (-6, -191), (-9, -127), and (-31, -37).
Common Mistakes and How to Avoid Them in Factors of 1146
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 1146, 1 and 1146 are also factors.
Factors of 1146 Examples
Problem 1
There are 573 students in a school and 2 buses. How will they divide the students equally?
They will have 286.5 students in each bus, but since students cannot be halved, they should distribute them with 286 in one bus and 287 in the other.
Explanation
To divide the students equally, we need to divide the total students by the number of buses.
573/2 = 286.5.
Problem 2
A garden is rectangular, the length of the garden is 31 meters and the total area is 1146 square meters. Find the width.
37 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1146 = 31 × width
To find the value of width, shift 31 to the left side.
1146/31 = width
Width = 37.
Problem 3
There are 6 teams and 1146 people. How many people will be in each team?
Each team will have 191 people.
Explanation
To find the number of people in each team, divide the total number of people by the teams.
1146/6 = 191.
Problem 4
In a class, there are 1146 students, and 3 sections. How many students are there in each section?
There are 382 students in each section.
Explanation
Dividing the students by the total sections, we will get the number of students in each section.
1146/3 = 382.
Problem 5
1146 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 127 books.
Explanation
Divide total books by shelves.
1146/9 = 127.
FAQs on Factors of 1146
1.What are the factors of 1146?
2.Mention the prime factors of 1146.
3.Is 1146 a multiple of 9?
4.Mention the factor pairs of 1146.
5.What is the square of 1146?
Important Glossaries for Factors of 1146
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1146 are 1, 2, 3, 6, 9, 31, 37, and 1146.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 191 are prime factors of 1146.
- 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 1146 are (1, 1146), (2, 573), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For 1146, it is 2 × 3 × 191.
- Multiple: A number that can be divided by another number without a remainder. For example, 1146 is a multiple of 9.
Explore More numbers
Previous to Factors of 1146
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.
