107 LearnersLast updated on May 26th, 2025
Factors of 621
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 621, how they are used in real life, and tips to learn them quickly.
What are the Factors of 621?
The numbers that divide 621 evenly are known as factors of 621. A factor of 621 is a number that divides the number without a remainder. The factors of 621 are 1, 3, 9, 23, 27, 69, 207, and 621.
Negative factors of 621: -1, -3, -9, -23, -27, -69, -207, and -621.
Prime factors of 621: 3 and 23.
Prime factorization of 621: 3 × 3 × 69, with 69 being 3 × 23. Therefore, 621 = 3² × 23.
The sum of factors of 621: 1 + 3 + 9 + 23 + 27 + 69 + 207 + 621 = 960
How to Find Factors of 621?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 621. Identifying the numbers which are multiplied to get the number 621 is the multiplication method.
Step 1: Multiply 621 by 1, 621 × 1 = 621.
Step 2: Check for other numbers that give 621 after multiplying
3 × 207 = 621
9 × 69 = 621
23 × 27 = 621
Therefore, the positive factor pairs of 621 are: (1, 621), (3, 207), (9, 69), (23, 27). 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 621 by 1, 621 ÷ 1 = 621.
Step 2: Continue dividing 621 by the numbers until the remainder becomes 0.
621 ÷ 1 = 621
621 ÷ 3 = 207
621 ÷ 9 = 69
621 ÷ 23 = 27
Therefore, the factors of 621 are: 1, 3, 9, 23, 27, 69, 207, 621.
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 621 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
621 ÷ 3 = 207
207 ÷ 3 = 69
69 ÷ 3 = 23
23 ÷ 23 = 1
The prime factors of 621 are 3 and 23. The prime factorization of 621 is: 3² × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 621 is divided by 3 to get 207.
Step 2: Now divide 207 by 3 to get 69.
Step 3: Then divide 69 by 3 to get 23. Here, 23 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 621 is: 3² × 23.
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 621: (1, 621), (3, 207), (9, 69), (23, 27).
- Negative factor pairs of 621: (-1, -621), (-3, -207), (-9, -69), (-23, -27).
Common Mistakes and How to Avoid Them in Factors of 621
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 621, 1 and 621 are also factors.
Factors of 621 Examples
Problem 1
There are 9 students and 621 pages in a book. How will they divide the pages equally?
They will get 69 pages each.
Explanation
To divide the pages equally, we need to divide the total pages by the number of students.
621/9 = 69
Problem 2
A garden is rectangular, the length of the garden is 27 meters, and the total area is 621 square meters. Find the width?
23 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
621 = 27 × width To find the value of width, we need to shift 27 to the left side.
621/27 = width
Width = 23.
Problem 3
There are 3 schools and 621 students. How many students will be in each school?
Each school will have 207 students.
Explanation
To find the students in each school, divide the total students by the number of schools. 621/3 = 207
Problem 4
In a conference, there are 621 attendees, and 23 teams. How many attendees are there in each team?
There are 27 attendees in each team.
Explanation
Dividing the attendees by the total teams, we will get the number of attendees in each team. 621/23 = 27
Problem 5
621 chairs need to be arranged in 3 rows. How many chairs will go in each row?
Each of the rows has 207 chairs.
Explanation
Divide total chairs by rows. 621/3 = 207
FAQs on Factors of 621
1.What are the factors of 621?
2.Mention the prime factors of 621.
3.Is 621 a multiple of 9?
4.Mention the factor pairs of 621?
5.What is the cube of 621?
Important Glossaries for Factor of 621
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 621 are 1, 3, 9, 23, 27, 69, 207, and 621.
- Prime factors: The factors which are prime numbers. For example, 3 and 23 are prime factors of 621.
- 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 621 are (1, 621), (3, 207), etc.
- Prime factorization: Breaking down a composite number into a product of its prime factors. For example, the prime factorization of 621 is 3² × 23.
- Multiples: The result of multiplying a number by an integer. For example, 621 is a multiple of 9.
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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.
