125 LearnersLast updated on May 26th, 2025
Factors of 213
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 213, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 213?
The numbers that divide 213 evenly are known as factors of 213.
A factor of 213 is a number that divides the number without remainder.
The factors of 213 are 1, 3, 71, and 213.
Negative factors of 213: -1, -3, -71, and -213.
Prime factors of 213: 3 and 71.
Prime factorization of 213: 3 × 71.
The sum of factors of 213: 1 + 3 + 71 + 213 = 288
How to Find Factors of 213?
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 213. Identifying the numbers which are multiplied to get the number 213 is the multiplication method.
Step 1: Multiply 213 by 1, 213 × 1 = 213.
Step 2: Check for other numbers that give 213 after multiplying:
3 × 71 = 213
Therefore, the positive factor pairs of 213 are: (1, 213), (3, 71).
All these factor pairs result in 213.
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 as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 213 by 1, 213 ÷ 1 = 213.
Step 2: Continue dividing 213 by the numbers until the remainder becomes 0.
213 ÷ 1 = 213
213 ÷ 3 = 71
Therefore, the factors of 213 are: 1, 3, 71, 213.
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 213 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
213 ÷ 3 = 71
71 ÷ 71 = 1
The prime factors of 213 are 3 and 71.
The prime factorization of 213 is: 3 × 71.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 213 is divided by 3 to get 71.
Here, 71 is a prime number, that cannot be divided anymore.
So, the prime factorization of 213 is: 3 × 71.
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 213: (1, 213), (3, 71).
Negative factor pairs of 213: (-1, -213), (-3, -71).
Common Mistakes and How to Avoid Them in Factors of 213
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 213, 1 and 213 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 213 consist of -1, -3, -71, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 213/1.5 = 142, 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 213 are prime numbers. For example, 3 and 71 are the prime factors of 213, but it has other factors like 1 and 213.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 213 as 3 × 71 and missing all the key factors.
Factors of 213 Examples
Problem 1
There are 3 groups and 213 apples. How will they divide it equally?
They will get 71 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of groups.
213/3 = 71
Problem 2
A rectangular garden has a length of 71 meters and a total area of 213 square meters. Find the width?
3 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
213 = 71 × width
To find the value of width, we need to shift 71 to the left side.
213/71 = width
Width = 3.
Problem 3
There are 71 students and 213 books. How many books will each student receive?
Each student will receive 3 books.
Explanation
To find the books each student will receive, divide the total books by the number of students.
213/71 = 3
FAQs on Factors of 213
1.What are the factors of 213?
2.Mention the prime factors of 213.
3.Is 213 a multiple of 3?
4.Mention the factor pairs of 213?
5.What is the square of 213?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 213?
7.What are some fun ways kids in United Kingdom can practice Factors of 213 with numbers?
8.What role do numbers and Factors of 213 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 213 skills?
Important Glossaries for Factors of 213
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 213 are 1, 3, 71, and 213.
- Prime factors: The factors which are prime numbers. For example, 3 and 71 are prime factors of 213.
- 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 213 are (1, 213) and (3, 71).
- Multiple: A multiple of a number is a product of that number and an integer. For example, 213 is a multiple of 3.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 213 is 3 × 71.
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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.
