203 LearnersLast updated on May 26th, 2025
Factors of 329
Factors of 329 are those numbers that are divisible into 329, without leaving any 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 329 and the different methods to find them.
What are the Factors of 329?
The factors of 329 are the numbers that divide 329 evenly.
Positive Factors: These are the positive numbers that divide 329 evenly.
Positive factors are 1, 7, 47, and 329.
Negative Factors: The negative values of the factors of a number.
Negative factors are -1, -7, -47, -329
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 329 as the product.
Prime factors: 7, 47
Prime Factorization: Prime factorization involves breaking 329 into its prime factors.
It is expressed as 7 × 47
Table listing the factors of 329
|
Positive Factors |
1, 7, 47, 329 |
|
Negative Factors |
-1, -7, -47, -329 |
|
Prime Factors |
7, 47 |
|
Prime Factorization |
71 x 471 |
This breakdown helps in understanding the various factors of 329, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 329?
There are various methods to find the factors of a particular number.
Methods to find the factors of 329:
- 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 329 as their product.
Step 1: Find the pair of numbers whose product is 329.
Step 2: The factors are those numbers, when multiplied, give 329.
Step 3: Make a list of numbers whose product will be 329.
A list of numbers whose products are 329 is given below:
- 1 × 329 = 329
- 7 × 47 = 329
Thus, the factors of 329 are 1, 7, 47, and 329
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: 329÷1 = 329
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 329 are 1, 7, 47, and 329
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 329: Number 329 has only two prime factors.
Prime factors of 329 are 7and 47.
To find the prime factors of 329, we can divide 329 with the prime numbers like 7 and 47 from the list of factors of 329.
Step 1: 329 is to be divided with a prime number. 329 ÷ 7 = 47.
Step 2: The product obtained i.e., 47 also should be divided with a prime number.47 ÷ 47 =1
Prime Factorization of 329: The simplification of 329 using the prime factors of 329 from the factors 329 has.
Expressed as 7 × 47
Factor Tree
The prime factorization of a number can be represented visually by 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 329 into its prime factors: 71 x 471
Positive and Negative Factor Pairs of 329
Factors of 329 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, 329), (7, 47)
Negative Factor Pairs: (-1, -329), (-7, -47)
Common Mistakes and How to Avoid Them in Factors of 329
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 47 as a non-factor.
When 47 is multiplied by 7 (47 × 7), we get 329 as the product. Hence, 47 is a factor of 329. Kids can find it difficult to understand that larger numbers like 47 can be factors. Always remember that factors are whole numbers that will divide the given number completely, whether it's a single-digit or two-digit number.
Solved Examples for Factors of 329
Problem 1
Can you check whether 329 and 11 are co-prime?
Yes, 329 and 11 are 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 329: 1, 7, 47, 329
Factors of 11: 1, 11
Here, the GCF is 1. So 329 and 11 are co-prime. For co-prime numbers, the GCF should be 1.
Problem 2
Verify whether 329 is a multiple of 47
Yes, 329 is a multiple of 47
Explanation
A multiple of 47 is any number that can be obtained by multiplying 47 by another whole number. Since 47 × 7 = 329, it shows that 329 is a multiple of 47.
Problem 3
Identify the perfect square from the factors of 329
The perfect square factor of 329 is 1
Explanation
A perfect square is a number we get when the same number is multiplied twice. Among the factors of 329, 1 is the only perfect square, as 1 × 1 = 1.
Problem 4
List the factors of 329
The factors of 329 are 1, 7, 47, and 329
Explanation
Factors are numbers that divide evenly into another number. For 329, the numbers 1, 7, 47, and 329 divide 329 without a remainder.
Problem 5
Can 329 be classified as a prime number?
329 cannot be a prime number.
Explanation
329 has got 4 factors, the additional factors are 7 and 47. So it is not a prime number.
FAQ’s for Factors of 329
1.What are the factors of 329?
2.How do you determine if a number is a factor of 329?
3.What is the smallest factor of 329?
4.What is the largest factor of 329?
5.How many factors does 329 have?
6.How many odd factors does 329 have?
7.What factors go into 329?
8.Do any perfect squares exist in the factors of 329?
Glossaries for Factors of 329
- Factors: Numbers that divide a given number completely, leaving no remainder.
- Prime Factors: Prime numbers from the list of factors of a particular number, when multiplied together, give the original number.
- Prime Factorization: The process of breaking down a number into its prime factors and expressing it as a product of prime numbers.
- Factor Tree: A visual tool used to represent the prime factorization of a number by splitting it into its prime factors.
- Multiple: A number that results from multiplying a given number by an integer.
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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.
