139 LearnersLast updated on May 28th, 2025
Factors of 1311
Factors are the numbers that divide any 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 1311, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1311?
The numbers that divide 1311 evenly are known as factors of 1311.
A factor of 1311 is a number that divides the number without a remainder.
The factors of 1311 are 1, 3, 19, 23, 57, 69, 437, and 1311.
Negative factors of 1311: -1, -3, -19, -23, -57, -69, -437, and -1311.
Prime factors of 1311: 3, 19, and 23.
Prime factorization of 1311: 3 × 19 × 23.
The sum of factors of 1311: 1 + 3 + 19 + 23 + 57 + 69 + 437 + 1311 = 1919
How to Find Factors of 1311?
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 1311. Identifying the numbers which are multiplied to get the number 1311 is the multiplication method.
Step 1: Multiply 1311 by 1, 1311 × 1 = 1311.
Step 2: Check for other numbers that give 1311 after multiplying
3 × 437 = 1311
19 × 69 = 1311
23 × 57 = 1311
Therefore, the positive factor pairs of 1311 are: (1, 1311), (3, 437), (19, 69), and (23, 57).
All these factor pairs result in 1311.
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 in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 1311 by 1, 1311 ÷ 1 = 1311.
Step 2: Continue dividing 1311 by the numbers until the remainder becomes 0.
1311 ÷ 1 = 1311
1311 ÷ 3 = 437
1311 ÷ 19 = 69
1311 ÷ 23 = 57
Therefore, the factors of 1311 are: 1, 3, 19, 23, 57, 69, 437, 1311.
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 1311 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1311 ÷ 3 = 437
437 ÷ 19 = 23
23 ÷ 23 = 1
The prime factors of 1311 are 3, 19, and 23.
The prime factorization of 1311 is: 3 × 19 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1311 is divided by 3 to get 437.
Step 2: Now divide 437 by 19 to get 23.
Step 3: Here, 23 is a prime number and cannot be divided further.
So, the prime factorization of 1311 is: 3 × 19 × 23.
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 1311: (1, 1311), (3, 437), (19, 69), and (23, 57).
Negative factor pairs of 1311: (-1, -1311), (-3, -437), (-19, -69), and (-23, -57).
Common Mistakes and How to Avoid Them in Factors of 1311
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 1311, 1 and 1311 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1311 consist of -1, -3, -19, etc.
Mistake 3
Including the Fraction
People might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1311/1.5 = 874, and it 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 1311 are prime numbers.
For example, 3, 19, and 23 are the prime factors of 1311, but it has other factors like 57, 69.
Mistake 5
Mistake in Factorization
People might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1311 as 3 × 19 × 23 and missing all the key factors.
Factors of 1311 Examples
Problem 1
A teacher wants to divide 1311 pencils equally among 3 classes. How many pencils will each class receive?
Each class will receive 437 pencils.
Explanation
To divide the pencils equally, we need to divide the total pencils by the number of classes.
1311/3 = 437
Problem 2
A rectangular garden has an area of 1311 square meters, and the length is 69 meters. Find the width.
19 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1311 = 69 × width
To find the value of width, we need to shift 69 to the left side.
1311/69 = width
Width = 19.
Problem 3
A farmer has 1311 apples and wants to put them in 19 baskets. How many apples will be in each basket?
Each basket will have 69 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
1311/19 = 69
Problem 4
A company has 1311 projects and 23 teams. How many projects are assigned to each team?
There are 57 projects assigned to each team.
Explanation
Dividing the projects by the total number of teams, we get the number of projects assigned to each team.
1311/23 = 57
Problem 5
1311 books need to be distributed equally among 1311 schools. How many books will go to each school?
Each school will receive 1 book.
Explanation
Divide the total books by the number of schools.
1311/1311 = 1
FAQs on Factors of 1311
1.What are the factors of 1311?
2.Mention the prime factors of 1311.
3.Is 1311 a multiple of 19?
4.Mention the factor pairs of 1311?
5.What is the square of 1311?
Important Glossaries for Factors of 1311
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1311 are 1, 3, 19, 23, 57, 69, 437, and 1311.
- Prime factors: The factors which are prime numbers. For example, 3, 19, and 23 are prime factors of 1311.
- 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 1311 are (1, 1311), (3, 437), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1311 is 3 × 19 × 23.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 1311 is a multiple of 3, 19, and 23.
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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.
