103 LearnersLast updated on May 26th, 2025
Factors of 405
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 405, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 405?
The numbers that divide 405 evenly are known as factors of 405.
A factor of 405 is a number that divides the number without remainder.
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, and 405.
Negative factors of 405: -1, -3, -5, -9, -15, -27, -45, -81, -135, and -405.
Prime factors of 405: 3 and 5.
Prime factorization of 405: 34 × 5.
The sum of factors of 405: 1 + 3 + 5 + 9 + 15 + 27 + 45 + 81 + 135 + 405 = 726
How to Find Factors of 405?
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 405. Identifying the numbers which are multiplied to get the number 405 is the multiplication method.
Step 1: Multiply 405 by 1, 405 × 1 = 405.
Step 2: Check for other numbers that give 405 after multiplying 3 × 135 = 405 5 × 81 = 405 9 × 45 = 405 15 × 27 = 405
Therefore, the positive factor pairs of 405 are: (1, 405), (3, 135), (5, 81), (9, 45), (15, 27).
All these factor pairs result in 405.
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 in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 405 by 1, 405 ÷ 1 = 405.
Step 2: Continue dividing 405 by the numbers until the remainder becomes 0.
405 ÷ 1 = 405
405 ÷ 3 = 135
405 ÷ 5 = 81
405 ÷ 9 = 45
405 ÷ 15 = 27
Therefore, the factors of 405 are: 1, 3, 5, 9, 15, 27, 45, 81, 135, 405.
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 405 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 405 are 3 and 5.
The prime factorization of 405 is: 34 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 405 is divided by 3 to get 135.
Step 2: Now divide 135 by 3 to get 45.
Step 3: Then divide 45 by 3 to get 15.
Step 4: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 405 is: 34 × 5.
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 405: (1, 405), (3, 135), (5, 81), (9, 45), and (15, 27).
Negative factor pairs of 405: (-1, -405), (-3, -135), (-5, -81), (-9, -45), and (-15, -27).
Common Mistakes and How to Avoid Them in Factors of 405
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 405, 1 and 405 is also a factor.
Factors of 405 Examples
Problem 1
There are 9 teams and 405 candies. How will they divide it equally?
They will get 45 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of teams.
405/9 = 45
Problem 2
A rectangular garden has a length of 15 meters and a total area of 405 square meters. Find the width.
27 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 405 = 15 × width
To find the value of width, we need to shift 15 to the left side.
405/15 = width
Width = 27.
Problem 3
There are 27 boxes and 405 marbles. How many marbles will be in each box?
Each box will have 15 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
405/27 = 15
Problem 4
In a hall, there are 405 chairs, and 5 sections. How many chairs are there in each section?
There are 81 chairs in each section.
Explanation
Dividing the chairs with the total sections, we will get the number of chairs in each section.
405/5 = 81
Problem 5
405 books need to be arranged in 15 shelves. How many books will go on each shelf?
Each of the shelves has 27 books.
Explanation
Divide total books with shelves.
405/15 = 27
FAQs on Factors of 405
1.What are the factors of 405?
2.Mention the prime factors of 405.
3.Is 405 a multiple of 9?
4.Mention the factor pairs of 405?
5.What is the square of 405?
6.How can children in India use numbers in everyday life to understand Factors of 405?
7.What are some fun ways kids in India can practice Factors of 405 with numbers?
8.What role do numbers and Factors of 405 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 405 skills?
Important Glossaries for Factor of 405
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, and 405.
- Prime factors: The factors which are prime numbers. For example, 3 and 5 are prime factors of 405.
- 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 405 are (1, 405), (3, 135), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 405 is 3^4 × 5.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to the target number. For example, using this method to find factors of 405.
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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
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