182 LearnersLast updated on May 26th, 2025
Factors of 328
Factors of 328 are numbers that can divide 328 completely without the remainder. We often use factors like organizing events and seating arrangements in our daily lives. In this topic, we will know more about the factors of 328 and the different methods to find them.
What are the Factors of 328?
The factors of 328 are the numbers that divide 328 evenly.
Positive Factors: These are the positive numbers that divide 342 evenly.
Positive factors are 1, 2, 4, 8, 41, 82, 164, and 328.
Negative Factors: The negative values of the factors of a number.
Negative factors: -1, -2, -4, -8, -41, -82, -164, -328
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 328 as the product.
Prime factors: 2, 41
Prime Factorization: Prime factorization involves breaking 328 into its prime factors.
It is expressed as 2³ × 411
Table Listing the Factors of 328
|
Positive Factors |
1, 2, 4, 8, 41, 82, 164, 328 |
|
Negative Factors |
-1, -2, -4, -8, -41, -82, -164, -328 |
|
Prime Factors |
2, 41 |
|
Prime Factorization |
2³ × 411 |
This breakdown helps in understanding the various factors of 328, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 328?
To find the factors of 328, there are various methods. Such as:
Methods to find the factors of 328:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair of factors that give 328 as their product.
Step 1: Find the pair of numbers whose product is 328.
Step 2: The factors are those numbers, when multiplied, give 328.
Step 3: Make a list of numbers whose product will be 328.
A list of numbers whose products are 328 is given below:
- 1 × 328 = 328
- 2 × 164 = 328
- 4 × 82 = 328
- 8 × 41 = 328
Thus, the factors of 328 are 1, 2, 4, 8, 41, 82, 164, and 328.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number. The steps are given below:
Step 1: Since every number is divisible by 1, 1 will always be a factor.
Example: 328 ÷ 1 = 328
Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.
Thus, the factors of 328 are 1, 2, 4, 8, 41, 82, 164, and 328.Thus, the factors of 328 are 1, 2, 4, 8, 41, 82, 164, and 328.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number when it is simplified using the factors of that number and is expressed in the form of prime factors is the prime factorization of a number.
Prime Factors of 328: Number 328 has two prime factors.
Prime factors of 328: 2, 41
To find the prime factors of 328, we can divide 328 with the prime numbers like 2 and 41 from the list of factors of 328.
Step 1: Divide 328 with the prime number 2
- 328 ÷ 2 = 164
Step 2: Divide 164 with the prime number 2
- 164 ÷ 2 = 82
Step 3: Divide 82 with the prime number 2
- 82 ÷ 2 = 41
Step 4: Divide 41 by 41
- 41 ÷ 41 = 1
Prime Factorization of 328: Prime Factorization breaks down the prime factors of 328
Expressed as 2³ × 411
Factor Tree
The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.
This tree shows the breakdown of 328 into its prime factors: 23 x 41
Positive and Negative Factor Pairs of 328
Factors of 328 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.
Positive Factor Pairs: (1, 328), (2, 164), (4, 82), (8, 41)
Negative Factor Pairs: (-1, -328), (-2, -164), (-4, -82), (-8, -41)
Common Mistakes and How to Avoid Them in Factors of 328
Mistakes can occur while finding the factors. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below.
Mistake 1
Assuming 2 is the only factor of 328
Since numbers divisible by 2 may lead to the assumption that 2 is the only factor, it's essential to check for other factors like 1, 4, 8, 41, 82, and 164.
Factors of 328 Examples
Problem 1
Can you check whether 328 and 164 are co-prime?
No, 328 and 164 are not co-prime.
Explanation
To check whether two numbers are co-prime, list their factors first. Once you have listed the factors, identify the common factors and determine the GCF. If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 328: 1, 2, 4, 8, 41, 82, 164, 328
Factors of 164: 1, 2, 4, 41, 82, 164
Here, the GCF is 164. So, 328 and 164 are not co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 328 is a multiple of 8.
Yes, 328 is a multiple of 8.
Explanation
Multiples of 8 are numbers we get when 8 is multiplied by another number. When 328 is divided by 8, the quotient is 41, showing that 328 is a multiple of 8.
Problem 3
Identify the perfect square from the factors of 328.
The perfect square factor of 328 is 4 and the root is 2.
Explanation
A perfect square is a number we get when the same number is multiplied twice. When 2 is multiplied twice (2×2), we get the perfect square 4, which is a factor of 328.
Problem 4
What is the least common factor (LCF) of 328 and 164?
The least common factor (LCF) of 328 and 164 is 1.
Explanation
The least common factor of any two numbers is always 1 unless the numbers are the same. Since the only common factor between 328 and 164 is 1, the LCF is 1.
Problem 5
Are 328 and 164 divisible by 41?
Yes, both 328 and 164 are divisible by 41.
Explanation
To check divisibility by 41, divide both numbers by 41. When 328 is divided by 41, the quotient is 8, and when 164 is divided by 41, the quotient is 4. Therefore, both numbers are divisible by 41.
FAQs on Factors of 328
1.What are the factors of 328?
2.How do you determine if a number is a factor of 328?
3.What is the smallest factor of 328?
4.What is the largest factor of 328?
5.How many factors does 328 have?
6.How many odd factors does 328 have?
7.What factors go into 328?
8.Do any perfect squares exist in the factors of 328?
Important glossaries for the Factors of 328
- Factor: Numbers that divide another number completely without leaving a remainder. For example, the factors of 328 are 1, 2, 4, 8, 41, 82, 164, and 328.
- Prime Factorization: The process of breaking down a number into its prime factors and expressing it as a product of prime numbers. For 328, its prime factorization is expressed as 2³ × 41.
- Co-prime: Numbers that have only 1 as their common factor. For example, 328 and 164 are not co-prime because their greatest common factor (GCF) is 164.
- Multiple: A number that is a product of a given number and another integer. For instance, 328 is a multiple of 8 since 328 ÷ 8 = 41.
- Perfect Square: A number that is the product of a whole number multiplied by itself. For example, 4 is a perfect square factor of 328, as 2 × 2 = 4.
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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.
