100 LearnersLast updated on May 26th, 2025
Factors of 408
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 408, how they are used in real life, and tips to learn them quickly.
What are the Factors of 408?
The numbers that divide 408 evenly are known as factors of 408.
A factor of 408 is a number that divides the number without a remainder.
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, and 408.
Negative factors of 408: -1, -2, -3, -4, -6, -8, -12, -17, -24, -34, -51, -68, -102, -136, -204, and -408.
Prime factors of 408: 2, 3, and 17.
Prime factorization of 408: 2³ × 3 × 17.
The sum of factors of 408: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 17 + 24 + 34 + 51 + 68 + 102 + 136 + 204 + 408 = 1080
How to Find Factors of 408?
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 408. Identifying the numbers which are multiplied to get the number 408 is the multiplication method.
Step 1: Multiply 408 by 1, 408 × 1 = 408.
Step 2: Check for other numbers that give 408 after multiplying:
2 × 204 = 408
3 × 136 = 408
4 × 102 = 408
6 × 68 = 408
8 × 51 = 408
12 × 34 = 408
17 × 24 = 408
Therefore, the positive factor pairs of 408 are: (1, 408), (2, 204), (3, 136), (4, 102), (6, 68), (8, 51), (12, 34), (17, 24).
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 as whole numbers as factors. Factors can be calculated by following the simple division method:
Step 1: Divide 408 by 1, 408 ÷ 1 = 408.
Step 2: Continue dividing 408 by the numbers until the remainder becomes 0.
408 ÷ 1 = 408
408 ÷ 2 = 204
408 ÷ 3 = 136
408 ÷ 4 = 102
408 ÷ 6 = 68
408 ÷ 8 = 51
408 ÷ 12 = 34
408 ÷ 17 = 24
Therefore, the factors of 408 are: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408.
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 408 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
408 ÷ 2 = 204
204 ÷ 2 = 102
102 ÷ 2 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
The prime factors of 408 are 2, 3, and 17. The prime factorization of 408 is: 2³ × 3 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 408 is divided by 2 to get 204.
Step 2: Now divide 204 by 2 to get 102.
Step 3: Then divide 102 by 2 to get 51.
Step 4: Divide 51 by 3 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 408 is: 2³ × 3 × 17.
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 408: (1, 408), (2, 204), (3, 136), (4, 102), (6, 68), (8, 51), (12, 34), (17, 24).
Negative factor pairs of 408: (-1, -408), (-2, -204), (-3, -136), (-4, -102), (-6, -68), (-8, -51), (-12, -34), (-17, -24).
Common Mistakes and How to Avoid Them in Factors of 408
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 408, 1 and 408 are also factors.
Factors of 408 Examples
Problem 1
A group of 12 hikers plans to divide 408 energy bars equally. How many energy bars will each hiker receive?
Each hiker will receive 34 energy bars.
Explanation
To divide the energy bars equally, we need to divide the total energy bars by the number of hikers.
408/12 = 34
Problem 2
A rectangular garden has a length of 17 meters and a total area of 408 square meters. What is the width of the garden?
24 meters.
Explanation
To find the width of the garden, we use the formula: Area = length × width 408 = 17 × width
To find the value of width, we need to shift 17 to the left side.
408/17 = width
Width = 24.
Problem 3
There are 4 boxes and 408 marbles. How many marbles will be in each box?
Each box will have 102 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
408/4 = 102
Problem 4
In a school, there are 408 students and 34 groups. How many students are there in each group?
There are 12 students in each group.
Explanation
Dividing the students by the total number of groups, we will get the number of students in each group.
408/34 = 12
Problem 5
408 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 68 books.
Explanation
Divide the total number of books by the number of shelves.
408/6 = 68
FAQs on Factors of 408
1.What are the factors of 408?
2.Mention the prime factors of 408.
3.Is 408 a multiple of 6?
4.Mention the factor pairs of 408?
5.What is the square of 408?
6.How can children in India use numbers in everyday life to understand Factors of 408?
7.What are some fun ways kids in India can practice Factors of 408 with numbers?
8.What role do numbers and Factors of 408 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 408 skills?
Important Glossaries for Factor of 408
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, and 408.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 408.
- 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 408 are (1, 408), (2, 204), etc.
- Prime factorization: Breaking down a number into prime numbers that multiply to the original number. For example, the prime factorization of 408 is 2³ × 3 × 17.
- Multiple: A number that can be divided by another number without a remainder. For example, 408 is a multiple of 6.
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About BrightChamps in India
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.
