122 LearnersLast updated on May 26th, 2025
Factors of 214
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 214, how they are used in real life, and tips to learn them quickly.
What are the Factors of 214?
The numbers that divide 214 evenly are known as factors of 214.
A factor of 214 is a number that divides the number without remainder.
The factors of 214 are 1, 2, 107, and 214.
Negative factors of 214: -1, -2, -107, and -214.
Prime factors of 214: 2 and 107.
Prime factorization of 214: 2 × 107.
The sum of factors of 214: 1 + 2 + 107 + 214 = 324
How to Find Factors of 214?
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 214. Identifying the numbers which are multiplied to get the number 214 is the multiplication method.
Step 1: Multiply 214 by 1, 214 × 1 = 214.
Step 2: Check for other numbers that give 214 after multiplying
2 × 107 = 214
Therefore, the positive factor pairs of 214 are: (1, 214) and (2, 107).
All these factor pairs result in 214.
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 214 by 1, 214 ÷ 1 = 214.
Step 2: Continue dividing 214 by the numbers until the remainder becomes 0.
214 ÷ 1 = 214
214 ÷ 2 = 107
Therefore, the factors of 214 are: 1, 2, 107, 214.
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 214 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
214 ÷ 2 = 107
107 ÷ 107 = 1
The prime factors of 214 are 2 and 107.
The prime factorization of 214 is: 2 × 107
.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 214 is divided by 2 to get 107.
Step 2: Now divide 107 by 107 to get 1.
Here, 107 is a prime number and cannot be divided anymore.
So, the prime factorization of 214 is: 2 × 107.
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 214: (1, 214) and (2, 107).
Negative factor pairs of 214: (-1, -214) and (-2, -107).
Common Mistakes and How to Avoid Them in Factors of 214
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
People 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 214, 1 and 214 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 214 consist of -1, -2, etc.
Mistake 3
Including the Fraction
Sometimes fractions are mistakenly included as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 214/1.5 = 142.666..., 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 214 are prime numbers. For example, 2 and 107 are the prime factors of 214, but it has other factors like 1 and 214.
Mistake 5
Mistake in Factorization
Skipping steps in factorization can lead to incorrect factors.
For example, not breaking 214 as 2 × 107 and missing all the key factors.
Factors of 214 Examples
Problem 1
There are 2 teams and 214 apples. How will they divide them equally?
Each team will get 107 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of teams.
214/2 = 107
Problem 2
A room is rectangular, the length of the room is 2 meters and the total area is 214 square meters. Find the width?
107 meters.
Explanation
To find the width of the room, we use the formula, Area = length × width
214 = 2 × width
To find the value of width, we need to shift 2 to the left side.
214/2 = width
Width = 107.
Problem 3
There are 107 chairs and 214 people. How many people will sit on each chair?
Each chair will have 2 people.
Explanation
To find the number of people for each chair, divide the total people by the chairs.
214/107 = 2
Problem 4
In a school, there are 2 teachers and 214 students. How many students are there per teacher?
Each teacher has 107 students.
Explanation
Dividing the students by the total teachers, we will get the number of students per teacher.
214/2 = 107
Problem 5
214 books need to be distributed in 107 boxes. How many books will go in each box?
Each of the boxes has 2 books.
Explanation
Divide total books by boxes.
214/107 = 2
FAQs on Factors of 214
1.What are the factors of 214?
2.Mention the prime factors of 214.
3.Is 214 a multiple of 2?
4.Mention the factor pairs of 214?
5.What is the square of 214?
6.How can children in India use numbers in everyday life to understand Factors of 214?
7.What are some fun ways kids in India can practice Factors of 214 with numbers?
8.What role do numbers and Factors of 214 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 214 skills?
Important Glossaries for Factor of 214
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 214 are 1, 2, 107, and 214.
- Prime factors: The factors which are prime numbers. For example, 2 and 107 are prime factors of 214.
- 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 214 are (1, 214) and (2, 107).
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number.
- Division method: A method to find factors by dividing the number with integers to check which ones divide without remainder.
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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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