121 LearnersLast updated on May 26th, 2025
Factors of 212
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 212, how they are used in real life, and tips to learn them quickly.
What are the Factors of 212?
The numbers that divide 212 evenly are known as factors of 212.
A factor of 212 is a number that divides the number without a remainder.
The factors of 212 are 1, 2, 4, 53, 106, and 212.
Negative factors of 212: -1, -2, -4, -53, -106, and -212.
Prime factors of 212: 2 and 53.
Prime factorization of 212: (22 times 53).
The sum of factors of 212: 1 + 2 + 4 + 53 + 106 + 212 = 378.
How to Find Factors of 212?
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 212. Identifying the numbers which are multiplied to get the number 212 is the multiplication method.
Step 1: Multiply 212 by 1, 212 × 1 = 212.
Step 2: Check for other numbers that give 212 after multiplying
2 × 106 = 212
4 × 53 = 212
Therefore, the positive factor pairs of 212 are: (1, 212), (2, 106), and (4, 53).
All these factor pairs result in 212.
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 a simple division method -
Step 1: Divide 212 by 1, 212 ÷ 1 = 212.
Step 2: Continue dividing 212 by the numbers until the remainder becomes 0.
212 ÷ 1 = 212
212 ÷ 2 = 106
212 ÷ 4 = 53
Therefore, the factors of 212 are: 1, 2, 4, 53, 106, 212.
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 212 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
212 ÷ 2 = 106
106 ÷ 2 = 53
53 ÷ 53 = 1
The prime factors of 212 are 2 and 53.
The prime factorization of 212 is: (22 times 53).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 212 is divided by 2 to get 106.
Step 2: Now divide 106 by 2 to get 53.
Here, 53 is a prime number, that cannot be divided anymore.
So, the prime factorization of 212 is: (22 times 53).
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 212: (1, 212), (2, 106), and (4, 53).
Negative factor pairs of 212: (-1, -212), (-2, -106), and (-4, -53).
Common Mistakes and How to Avoid Them in Factors of 212
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 212, 1 and 212 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 212 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 212/1.5 = 141.333, 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 212 are prime numbers. For example, 2 and 53 are the prime factors of 212, but it has other factors like 4, 106.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 212 as (22 times 53) and missing all the key factors.
Factors of 212 Examples
Problem 1
There are 4 teams and 212 points to distribute. How many points will each team get?
Each team will get 53 points.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
212/4 = 53
Problem 2
A rectangular garden has a length of 2 meters and a total area of 212 square meters. Find the width.
106 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
212 = 2 × width
To find the value of width, we need to shift 2 to the left side.
212/2 = width
Width = 106.
Problem 3
There are 53 boxes and 212 apples. How many apples will be in each box?
Each box will have 4 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
212/53 = 4
Problem 4
In a conference, there are 212 attendees, and 2 sessions. How many attendees are there in each session?
There are 106 attendees in each session.
Explanation
Dividing the attendees by the total sessions, we will get the number of attendees in each session.
212/2 = 106
Problem 5
212 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has 53 books.
Explanation
Divide total books by shelves.
212/4 = 53
FAQs on Factors of 212
1.What are the factors of 212?
2.Mention the prime factors of 212.
3.Is 212 a multiple of 4?
4.Mention the factor pairs of 212?
5.What is the square of 212?
Important Glossaries for Factor of 212
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 212 are 1, 2, 4, 53, 106, and 212.
- Prime factors: The factors which are prime numbers. For example, 2 and 53 are prime factors of 212.
- 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 212 are (1, 212), (2, 106), etc.
- Prime factorization: Breaking down a number into the product of its prime factors. For instance, 212 can be expressed as (22 times 53).
- Multiplication method: A technique for finding factors by identifying pairs of numbers that multiply to give the original number.
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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.
