122 LearnersLast updated on May 26th, 2025
Factors of 1338
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 1338, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1338?
The numbers that divide 1338 evenly are known as factors of 1338.
A factor of 1338 is a number that divides the number without remainder.
The factors of 1338 are 1, 2, 3, 6, 223, 446, 669, and 1338.
Negative factors of 1338: -1, -2, -3, -6, -223, -446, -669, and -1338.
Prime factors of 1338: 2, 3, and 223.
Prime factorization of 1338: 2 × 3 × 223.
The sum of factors of 1338: 1 + 2 + 3 + 6 + 223 + 446 + 669 + 1338 = 2688
How to Find Factors of 1338?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1338. Identifying the numbers which are multiplied to get the number 1338 is the multiplication method.
Step 1: Multiply 1338 by 1, 1338 × 1 = 1338.
Step 2: Check for other numbers that give 1338 after multiplying
2 × 669 = 1338
3 × 446 = 1338
6 × 223 = 1338
Therefore, the positive factor pairs of 1338 are: (1, 1338), (2, 669), (3, 446), (6, 223).
All these factor pairs result in 1338.
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 1338 by 1, 1338 ÷ 1 = 1338.
Step 2: Continue dividing 1338 by the numbers until the remainder becomes 0.
1338 ÷ 1 = 1338
1338 ÷ 2 = 669
1338 ÷ 3 = 446
1338 ÷ 6 = 223
Therefore, the factors of 1338 are: 1, 2, 3, 6, 223, 446, 669, 1338.
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 1338 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1338 ÷ 2 = 669
669 ÷ 3 = 223
223 ÷ 223 = 1
The prime factors of 1338 are 2, 3, and 223.
The prime factorization of 1338 is: 2 × 3 × 223.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1338 is divided by 2 to get 669.
Step 2: Now divide 669 by 3 to get 223.
Step 3: Here, 223 is a prime number and cannot be divided further. So, the prime factorization of 1338 is: 2 × 3 × 223.
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 1338: (1, 1338), (2, 669), (3, 446), and (6, 223).
Negative factor pairs of 1338: (-1, -1338), (-2, -669), (-3, -446), and (-6, -223).
Common Mistakes and How to Avoid Them in Factors of 1338
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 1338, 1 and 1338 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 1338 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 1338/1.5 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 1338 are prime numbers. For instance, 2, 3, and 223 are the prime factors of 1338, but it has other factors like 6, 446.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1338 as 2 × 3 × 223 and missing all the key factors.
Factors of 1338 Examples
Problem 1
A group of 6 people has 1338 candies. How many candies will each person get if they divide them equally?
They will get 223 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of people.
1338/6 = 223
Problem 2
A rectangular garden has a length of 446 meters and a total area of 1338 square meters. Find the width.
3 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1338 = 446 × width
To find the value of width, we need to shift 446 to the left side.
1338/446 = width
Width = 3.
Problem 3
There are 669 chairs and 1338 students. How many students will sit on each chair?
Each chair will have 2 students.
Explanation
To find the number of students per chair, divide the total students by the chairs.
1338/669 = 2
Problem 4
In a classroom, there are 3 projectors and 1338 slides to present. How many slides will each projector show?
Each projector will show 446 slides.
Explanation
Dividing the slides by the total number of projectors, we get the number of slides per projector.
1338/3 = 446
Problem 5
1338 bricks need to be stacked in 223 piles. How many bricks will go in each pile?
Each pile will have 6 bricks.
Explanation
Divide total bricks by the number of piles.
1338/223 = 6
FAQs on Factors of 1338
1.What are the factors of 1338?
2.Mention the prime factors of 1338.
3.Is 1338 a multiple of 3?
4.Mention the factor pairs of 1338?
5.What is the square of 1338?
Important Glossaries for Factors of 1338
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1338 are 1, 2, 3, 6, 223, 446, 669, and 1338.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 223 are prime factors of 1338.
- 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 1338 are (1, 1338), (2, 669), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1338 is 2 × 3 × 223.
- Multiple: A number that can be divided by another number without a remainder. For example, 1338 is a multiple of 3.
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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.
