100 LearnersLast updated on May 26th, 2025
Factors of 414
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 414, how they are used in real life, and tips to learn them quickly.
What are the Factors of 414?
The numbers that divide 414 evenly are known as factors of 414.
A factor of 414 is a number that divides the number without a remainder.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, and 414.
Negative factors of 414: -1, -2, -3, -6, -9, -18, -23, -46, -69, -138, -207, and -414.
Prime factors of 414: 2, 3, and 23.
Prime factorization of 414: 2 × 3 × 3 × 23.
The sum of factors of 414: 1 + 2 + 3 + 6 + 9 + 18 + 23 + 46 + 69 + 138 + 207 + 414 = 936
How to Find Factors of 414?
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 414. Identifying the numbers which are multiplied to get the number 414 is the multiplication method.
Step 1: Multiply 414 by 1, 414 × 1 = 414.
Step 2: Check for other numbers that give 414 after multiplying
2 × 207 = 414
3 × 138 = 414
6 × 69 = 414
9 × 46 = 414
18 × 23 = 414
Therefore, the positive factor pairs of 414 are: (1, 414), (2, 207), (3, 138), (6, 69), (9, 46), and (18, 23).
All these factor pairs result in 414.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with 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 a simple division method
Step 1: Divide 414 by 1, 414 ÷ 1 = 414.
Step 2: Continue dividing 414 by the numbers until the remainder becomes 0.
414 ÷ 1 = 414
414 ÷ 2 = 207
414 ÷ 3 = 138
414 ÷ 6 = 69
414 ÷ 9 = 46
414 ÷ 18 = 23
Therefore, the factors of 414 are: 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 414 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
414 ÷ 2 = 207
207 ÷ 3 = 69
69 ÷ 3 = 23
23 ÷ 23 = 1
The prime factors of 414 are 2, 3, and 23.
The prime factorization of 414 is: 2 × 3 × 3 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 414 is divided by 2 to get 207.
Step 2: Now divide 207 by 3 to get 69.
Step 3: Then divide 69 by 3 to get 23. Here, 23 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 414 is: 2 × 3 × 3 × 23.
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 414: (1, 414), (2, 207), (3, 138), (6, 69), (9, 46), and (18, 23).
Negative factor pairs of 414: (-1, -414), (-2, -207), (-3, -138), (-6, -69), (-9, -46), and (-18, -23).
Common Mistakes and How to Avoid Them in Factors of 414
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 414, 1 and 414 are also factors.
Factors of 414 Examples
Problem 1
There are 12 friends and 414 candies. How will they divide it equally?
They will get 34.5 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
414/12 = 34.5
Problem 2
A garden is rectangular, the length of the garden is 18 meters, and the total area is 414 square meters. Find the width.
23 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
414 = 18 × width
To find the value of width, we need to shift 18 to the left side.
414/18 = width
Width = 23.
Problem 3
There are 69 backpacks and 414 pencils. How many pencils will be in each backpack?
Each backpack will have 6 pencils.
Explanation
To find the pencils in each backpack, divide the total pencils by the backpacks.
414/69 = 6
Problem 4
In a class, there are 414 students, and 23 groups. How many students are there in each group?
There are 18 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
414/23 = 18
Problem 5
414 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 46 books.
Explanation
Divide total books by shelves.
414/9 = 46
FAQs on Factors of 414
1.What are the factors of 414?
2.Mention the prime factors of 414.
3.Is 414 a multiple of 6?
4.Mention the factor pairs of 414?
5.What is the square of 414?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 414?
7.What are some fun ways kids in United Kingdom can practice Factors of 414 with numbers?
8.What role do numbers and Factors of 414 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 414 skills?
Important Glossaries for Factors of 414
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, and 414.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 23 are prime factors of 414.
- 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 414 are (1, 414), (2, 207), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 414 is 2 × 3 × 3 × 23.
- Multiple: A number that can be divided by another number without a remainder. For example, 414 is a multiple of 6.
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About BrightChamps in United Kingdom
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.
