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 214, how they are used in real life, and tips to learn them quickly.
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
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 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.
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.
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 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
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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).
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 2 teams and 214 apples. How will they divide them equally?
Each team will get 107 apples.
To divide the apples equally, we need to divide the total apples by the number of teams.
214/2 = 107
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.
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.
There are 107 chairs and 214 people. How many people will sit on each chair?
Each chair will have 2 people.
To find the number of people for each chair, divide the total people by the chairs.
214/107 = 2
In a school, there are 2 teachers and 214 students. How many students are there per teacher?
Each teacher has 107 students.
Dividing the students by the total teachers, we will get the number of students per teacher.
214/2 = 107
214 books need to be distributed in 107 boxes. How many books will go in each box?
Each of the boxes has 2 books.
Divide total books by boxes.
214/107 = 2
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.