110 LearnersLast updated on May 26th, 2025
Factors of 654
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 654, how they are used in real life, and tips to learn them quickly.
What are the Factors of 654?
The numbers that divide 654 evenly are known as factors of 654. A factor of 654 is a number that divides the number without remainder. The factors of 654 are 1, 2, 3, 6, 109, 218, 327, and 654.
Negative factors of 654: -1, -2, -3, -6, -109, -218, -327, and -654.
Prime factors of 654: 2, 3, and 109.
Prime factorization of 654: 2 × 3 × 109.
The sum of factors of 654: 1 + 2 + 3 + 6 + 109 + 218 + 327 + 654 = 1320
How to Find Factors of 654?
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 654. Identifying the numbers which are multiplied to get the number 654 is the multiplication method.
Step 1: Multiply 654 by 1, 654 × 1 = 654.
Step 2: Check for other numbers that give 654 after multiplying
2 × 327 = 654
3 × 218 = 654
6 × 109 = 654
Therefore, the positive factor pairs of 654 are: (1, 654), (2, 327), (3, 218), (6, 109). All these factor pairs result in 654. 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 results as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 654 by 1, 654 ÷ 1 = 654.
Step 2: Continue dividing 654 by the numbers until the remainder becomes 0.
654 ÷ 1 = 654
654 ÷ 2 = 327
654 ÷ 3 = 218
654 ÷ 6 = 109
Therefore, the factors of 654 are: 1, 2, 3, 6, 109, 218, 327, 654.
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 654 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
654 ÷ 2 = 327
327 ÷ 3 = 109
109 ÷ 109 = 1
The prime factors of 654 are 2, 3, and 109. The prime factorization of 654 is: 2 × 3 × 109.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 654 is divided by 2 to get 327.
Step 2: Now divide 327 by 3 to get 109.
Step 3: Here, 109 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 654 is: 2 × 3 × 109.
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 654: (1, 654), (2, 327), (3, 218), and (6, 109).
- Negative factor pairs of 654: (-1, -654), (-2, -327), (-3, -218), and (-6, -109).
Common Mistakes and How to Avoid Them in Factors of 654
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 factors for every number. Always remember to include 1 and the number itself. For example, in factors of 654, 1 and 654 are also factors.
Factors of 654 Examples
Problem 1
There are 6 teams and 654 players. How will they be divided equally?
Each team will have 109 players.
Explanation
To divide the players equally, we need to divide the total players by the number of teams.
654/6 = 109
Problem 2
A rectangular garden has a width of 3 meters and a total area of 654 square meters. Find the length?
218 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
654 = length × 3
To find the value of length, we need to shift 3 to the left side.
654/3 = length
Length = 218.
Problem 3
There are 327 seats and 2 sections. How many seats will be in each section?
Each section will have 163.5 seats, but since seats cannot be fractional, each section will have 163 or 164 seats.
Explanation
To find the seats in each section, divide the total seats by the sections.
327/2 = 163.5
Problem 4
A school has 654 students, and there are 109 classes. How many students are there in each class?
There are 6 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
654/109 = 6
Problem 5
654 chairs need to be arranged in 327 rows. How many chairs will go in each row?
Each row will have 2 chairs.
Explanation
Divide total chairs by rows.
654/327 = 2
FAQs on Factors of 654
1.What are the factors of 654?
2.Mention the prime factors of 654.
3.Is 654 a multiple of 3?
4.Mention the factor pairs of 654?
5.What is the square of 654?
Important Glossaries for Factor of 654
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 654 are 1, 2, 3, 6, 109, 218, 327, and 654.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 109 are prime factors of 654.
- 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 654 are (1, 654), (2, 327), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 654 is 2 × 3 × 109.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using multiplication to find factors of 654 like (2, 327).
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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.
