101 LearnersLast updated on May 26th, 2025
Factors of 398
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 398, how they are used in real life, and tips to learn them quickly.
What are the Factors of 398?
The numbers that divide 398 evenly are known as factors of 398.
A factor of 398 is a number that divides the number without remainder.
The factors of 398 are 1, 2, 199, and 398.
Negative factors of 398: -1, -2, -199, and -398.
Prime factors of 398: 2 and 199.
Prime factorization of 398: 2 × 199.
The sum of factors of 398: 1 + 2 + 199 + 398 = 600
How to Find Factors of 398?
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 398. Identifying the numbers which are multiplied to get the number 398 is the multiplication method.
Step 1: Multiply 398 by 1, 398 × 1 = 398.
Step 2: Check for other numbers that give 398 after multiplying 2 × 199 = 398
Therefore, the positive factor pairs of 398 are: (1, 398), (2, 199).
All these factor pairs result in 398.
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 the simple division method:
Step 1: Divide 398 by 1, 398 ÷ 1 = 398.
Step 2: Continue dividing 398 by the numbers until the remainder becomes 0.
398 ÷ 1 = 398
398 ÷ 2 = 199
Therefore, the factors of 398 are: 1, 2, 199, 398.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 398 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
398 ÷ 2 = 199
199 ÷ 199 = 1
The prime factors of 398 are 2 and 199.
The prime factorization of 398 is: 2 × 199.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 398 is divided by 2 to get 199.
Step 2: Since 199 is a prime number, it cannot be divided further.
So, the prime factorization of 398 is: 2 × 199.
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 398: (1, 398), (2, 199).
Negative factor pairs of 398: (-1, -398), (-2, -199).
Common Mistakes and How to Avoid Them in Factors of 398
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 398, 1 and 398 are also factors.
Factors of 398 Examples
Problem 1
There are 398 apples to be packed into boxes. Each box can hold 2 apples. How many boxes are needed?
199 boxes are needed.
Explanation
To find how many boxes are needed, we divide the total number of apples by the number of apples each box can hold.
398/2 = 199
Problem 2
A rectangular garden has a length of 199 meters and a total area of 398 square meters. Find the width of the garden.
2 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 398 = 199 × width
To find the value of width, we need to shift 199 to the left side.
398/199 = width
Width = 2
Problem 3
There is a banquet with 398 guests and 199 tables. How many guests will sit at each table?
Each table will have 2 guests.
Explanation
To find the guests at each table, divide the total guests by the tables.
398/199 = 2
Problem 4
398 students are to be divided into 2 teams. How many students are there in each team?
There are 199 students in each team.
Explanation
Dividing the students by the total teams, we get the number of students in each team.
398/2 = 199
Problem 5
A bookshop has 398 books and wants to place them in shelves that can hold 199 books each. How many shelves are needed?
2 shelves are needed.
Explanation
Divide total books by books per shelf.
398/199 = 2
FAQs on Factors of 398
1.What are the factors of 398?
2.Mention the prime factors of 398.
3.Is 398 a multiple of 2?
4.Mention the factor pairs of 398?
5.What is the square of 398?
Important Glossaries for Factors of 398
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 398 are 1, 2, 199, and 398.
- Prime factors: The factors which are prime numbers. For example, 2 and 199 are the prime factors of 398.
- 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 398 are (1, 398) and (2, 199).
- Prime factorization: The expression of a number as the product of its prime factors. For example, 398 = 2 × 199.
- Multiple: A multiple is the product of a number and an integer. For example, 398 is a multiple of 2.
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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.
