Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 3 groups and 213 apples. How will they divide it equally?
They will get 71 apples each.
To divide the apples equally, we need to divide the total apples with the number of groups.
213/3 = 71
A rectangular garden has a length of 71 meters and a total area of 213 square meters. Find the width?
3 meters.
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.
There are 71 students and 213 books. How many books will each student receive?
Each student will receive 3 books.
To find the books each student will receive, divide the total books by the number of students.
213/71 = 3
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.
: She loves to read number jokes and games.