123 LearnersLast updated on May 26th, 2025
Factors of 814
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 814, how they are used in real life, and tips to learn them quickly.
What are the Factors of 814?
The numbers that divide 814 evenly are known as factors of 814.
A factor of 814 is a number that divides the number without remainder.
The factors of 814 are 1, 2, 407, and 814.
Negative factors of 814: -1, -2, -407, and -814.
Prime factors of 814: 2 and 407.
Prime factorization of 814: 2 × 407.
The sum of factors of 814: 1 + 2 + 407 + 814 = 1224
How to Find Factors of 814?
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 814. Identifying the numbers which are multiplied to get the number 814 is the multiplication method.
Step 1: Multiply 814 by 1, 814 × 1 = 814.
Step 2: Check for other numbers that give 814 after multiplying
2 × 407 = 814
Therefore, the positive factor pairs of 814 are: (1, 814) and (2, 407).
All these factor pairs result in 814.
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 a simple division method
Step 1: Divide 814 by 1, 814 ÷ 1 = 814.
Step 2: Continue dividing 814 by the numbers until the remainder becomes 0.
814 ÷ 1 = 814
814 ÷ 2 = 407
Therefore, the factors of 814 are: 1, 2, 407, 814.
Prime Factors and Prime Factorization
The factors can be found by dividing it by 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 814 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
814 ÷ 2 = 407
407 ÷ 407 = 1
The prime factors of 814 are 2 and 407.
The prime factorization of 814 is: 2 × 407.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 814 is divided by 2 to get 407.
Step 2: 407 is a prime number, so it cannot be divided further. So, the prime factorization of 814 is: 2 × 407.
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 814: (1, 814) and (2, 407).
Negative factor pairs of 814: (-1, -814) and (-2, -407).
Common Mistakes and How to Avoid Them in Factors of 814
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 word. Always remember to include 1 and the number itself.
For example, in factors of 814, 1 and 814 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 814 consist of -1, -2, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 is a factor, because 814/1.5 = 542.666, and it 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 814 are prime numbers.
For example, 2 and 407 are the prime factors of 814, but it has other factors like 1, 814.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 814 as 2 × 407 and missing key factors.
Factors of 814 Examples
Problem 1
There are 4 teams and 814 points. How will they distribute the points equally among the teams?
They cannot distribute the points equally as 814 is not divisible by 4.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
814/4 = 203.5, which is not a whole number.
Problem 2
A ribbon is 814 cm long. If it is cut into 2 equal parts, what will be the length of each part?
Each part will be 407 cm long.
Explanation
To find the length of each part, divide the total length by 2.
814/2 = 407
Problem 3
There are 407 apples and 2 boxes. How many apples will each box have if distributed equally?
Each box will have 203.5 apples, which means they cannot be divided equally into the boxes.
Explanation
To find the apples in each box, divide the total apples by the boxes.
407/2 = 203.5, which is not a whole number.
Problem 4
A company has 814 employees and wants to form groups of 2. How many groups can be formed?
407 groups can be formed.
Explanation
Dividing the employees by the group size gives the number of groups.
814/2 = 407
Problem 5
A piece of land is 814 square meters. If each plot is 1 square meter, how many plots are there?
There are 814 plots.
Explanation
Divide the total area by the size of one plot.
814/1 = 814
FAQs on Factors of 814
1.What are the factors of 814?
2.Mention the prime factors of 814.
3.Is 814 a multiple of 2?
4.Mention the factor pairs of 814.
5.What is the square of 814?
Important Glossaries for Factor of 814
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 814 are 1, 2, 407, and 814.
- Prime factors: The factors which are prime numbers. For example, 2 and 407 are prime factors of 814.
- 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 814 are (1, 814) and (2, 407).
- Multiplication method: A method to find factor pairs by identifying which numbers multiply together to form the given number.
- Division method: A technique in which a number is divided by whole numbers to find factors without remainders.
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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.
