117 LearnersLast updated on May 26th, 2025
Factors of 1362
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1362, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1362?
The numbers that divide 1362 evenly are known as factors of 1362.
A factor of 1362 is a number that divides the number without remainder.
The factors of 1362 are 1, 2, 3, 6, 227, 454, 681, and 1362.
Negative factors of 1362: -1, -2, -3, -6, -227, -454, -681, and -1362.
Prime factors of 1362: 2, 3, and 227.
Prime factorization of 1362: 2 × 3 × 227.
The sum of factors of 1362: 1 + 2 + 3 + 6 + 227 + 454 + 681 + 1362 = 2736
How to Find Factors of 1362?
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 1362. Identifying the numbers which are multiplied to get the number 1362 is the multiplication method.
Step 1: Multiply 1362 by 1, 1362 × 1 = 1362.
Step 2: Check for other numbers that give 1362 after multiplying
2 × 681 = 1362
3 × 454 = 1362
6 × 227 = 1362
Therefore, the positive factor pairs of 1362 are: (1, 1362), (2, 681), (3, 454), (6, 227).
All these factor pairs result in 1362.
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 1362 by 1, 1362 ÷ 1 = 1362.
Step 2: Continue dividing 1362 by the numbers until the remainder becomes 0.
1362 ÷ 1 = 1362
1362 ÷ 2 = 681
1362 ÷ 3 = 454
1362 ÷ 6 = 227
Therefore, the factors of 1362 are: 1, 2, 3, 6, 227, 454, 681, and 1362.
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 1362 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1362 ÷ 2 = 681
681 ÷ 3 = 227
227 ÷ 227 = 1
The prime factors of 1362 are 2, 3, and 227.
The prime factorization of 1362 is: 2 × 3 × 227.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1362 is divided by 2 to get 681.
Step 2: Now divide 681 by 3 to get 227.
Step 3: Here, 227 is a prime number that cannot be divided further. So, the prime factorization of 1362 is: 2 × 3 × 227.
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 1362: (1, 1362), (2, 681), (3, 454), (6, 227).
Negative factor pairs of 1362: (-1, -1362), (-2, -681), (-3, -454), (-6, -227).
Common Mistakes and How to Avoid Them in Factors of 1362
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1362, 1 and 1362 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 1362 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 1362/1.5 = 908, 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 1362 are prime numbers.
For example, 2, 3, and 227 are the prime factors of 1362, but it has other factors like 6, 454.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1362 as 2 × 3 × 227 and missing all the key factors.
Factors of 1362 Examples
Problem 1
There are 6 teams and 1362 points. How will they distribute the points equally?
Each team will get 227 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of teams.
1362/6 = 227
Problem 2
A conference room is rectangular, the width of the room is 3 meters and the total area is 1362 square meters. Find the length?
454 meters.
Explanation
To find the length of the room, we use the formula,
Area = length × width
1362 = length × 3
To find the value of the length, we need to shift 3 to the left side.
1362/3 = length
Length = 454.
Problem 3
There are 681 students and 3 buses. How many students will be in each bus?
Each bus will have 227 students.
Explanation
To find the students in each bus, divide the total students by the number of buses.
681/3 = 227
Problem 4
In a school, there are 1362 students, and 227 groups. How many students are there in each group?
There are 6 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1362/227 = 6
Problem 5
1362 books need to be arranged in 2 libraries. How many books will go in each library?
Each library will have 681 books.
Explanation
Divide total books by libraries.
1362/2 = 681
FAQs on Factors of 1362
1.What are the factors of 1362?
2.Mention the prime factors of 1362.
3.Is 1362 a multiple of 3?
4.Mention the factor pairs of 1362?
5.What is the square of 1362?
Important Glossaries for Factors of 1362
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1362 are 1, 2, 3, 6, 227, 454, 681, and 1362.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 227 are prime factors of 1362.
- 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 1362 are (1, 1362), (2, 681), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1362 is 2 × 3 × 227.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number, such as (1, 1362) for 1362.
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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.
