247 LearnersLast updated on May 26th, 2025
Factors of 364
Factors of 364 are numbers that can divide 364 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 364 and the different methods to find them.
What are the Factors of 364?
The factors of 364 are the numbers that divide 364 evenly.
Positive Factors: These are the positive numbers that divide, 364 evenly.
Positive factors are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364.
Negative Factors: The negative values of the factors of 4200 are:
Negative factors are -1, -2, -4, -7, -13, -14, -26, -28, -52, -91, -182, -364
Prime Factors: Prime factors are the prime numbers themselves that, when multiplied together, give 364 as the product.
Prime factors: 2, 7, 13
Prime Factorization: Prime factorization involves breaking 364 into its prime factors.
It is expressed as 22 × 71 × 131
Table Listing the Factors of 364
|
Positive Factors |
1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364 |
|
Negative Factors |
-1, -2, -4, -7, -13, -14, -26, -28, -52, -91, -182, -364 |
|
Prime Factors |
2, 7, 13 |
|
Prime Factorization |
22 × 71 × 131 |
This breakdown helps in understanding the various factors of 364, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 364?
There are different methods to find the factors of 364.
Methods to Find the Factors of 364:
- 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 364 as their product.
Step 1: Find the pair of numbers whose product is 364.
Step 2: The factors are those numbers, which when multiplied, give 364.
Step 3: Make a list of numbers whose product will be 364.
A list of numbers whose products are 364 is given below:
- 1 × 364 = 364
- 2 × 182 = 364
- 4 × 91 = 364
- 7 × 52 = 364
- 13 × 28 = 364
- 14 × 26 = 364
Thus, the factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364.
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: 364 ÷ 1 = 364
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 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364
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 364: Number 364 has three prime factors.
Prime factors of 364: 2, 7, 13
To find the prime factors of 364, we can divide 364 with the prime numbers like 2, 7, and 13 from the list of factors of 364.
Step 1: Divide 364 with the prime number 2
- 364 ÷ 2 = 182
Step 2: Divide 182 with the prime number 2
- 182 ÷ 2 = 91
Step 3: Divide 91 with the prime number 7
- 91 ÷ 7 = 13
Step 4: Divide 13 with the prime number 13
- 13 ÷ 13 = 1
Prime Factorization of 364: Prime factorization breaks down the prime factors of 364.
Expressed as 2² × 71 × 131.
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 364 into its prime factors: 2 × 7 × 13.
Positive and Negative Factor Pairs of 364
Factors of 364 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, 364), (2, 182), (4, 91), (7, 52), (13, 28), (14, 26)
Negative Factor Pairs: (-1, -364), (-2, -182), (-4, -91), (-7, -52), (-13, -28), (-14, -26)
Common Mistakes and How to Avoid Them in Factors of 364
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 7 as the only factor of 364
Since numbers like 7 divide 364 completely, you might assume that 7 is the only factor. Remember that factors are numbers that can divide the given number equally. Other numbers that can divide 364 completely include 1, 2, 4, 13, 14, 26, 28, 52, 91, 182, and 364.
Solved Examples For Factors of 364
Problem 1
Can you check whether 52 and 364 are co-prime?
No, 52 and 364 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 52: 1, 2, 4, 13, 26, 52
- Factors of 364: 1, 2, 4, 7, 13, 14, 28, 26, 52, 91, 182, 364
Here, the GCF is 52. So, 52 and 364 are not co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 364 is a multiple of 13
Yes, 364 is a multiple of 13
Explanation
Multiples of 13 are numbers we get when 13 is multiplied by another number. Since 13 × 28 = 364, 364 is a multiple of 13.
Problem 3
Identify the perfect square from the factors of 364
The perfect square factor of 364 is 1 and the root is 1
Explanation
A perfect square is a number we get when the same number is multiplied twice. In the factors of 364, the only perfect square is 1 (1 × 1).
Problem 4
Is 364 a prime number?
No, 364 is not a prime number
Explanation
Prime numbers are that, when multiplied together, give the original number. The factors of 364 are 1, 2, 4, 7, 13, 14, 28, 26, 52, 91, 182, and 364. Since 364 has more than two factors, it is not a prime number.
Problem 5
What is the greatest common factor (GCF) of 52 and 364?
The GCF of 52 and 364 is 52
Explanation
To find the GCF, list the factors of both numbers and identify the greatest factor common to both.
- Factors of 52: 1, 2, 4, 13, 26, 52
- Factors of 364: 1, 2, 4, 7, 13, 14, 28, 26, 52, 91, 182, 364
The greatest common factor between 52 and 364 is 52.
FAQ’s for Factors of 364
1.What are the factors of 364?
2.How do you determine if a number is a factor of 364?
3.What is the smallest factor of 364?
4.What is the largest factor of 364?
5.How many factors does 364 have?
6.How many odd factors does 364 have?
7.What factors go into 364?
8.Do any perfect squares exist in the factors of 364?
9.How can children in Qatar use numbers in everyday life to understand Factors of 364?
10.What are some fun ways kids in Qatar can practice Factors of 364 with numbers?
11.What role do numbers and Factors of 364 play in helping children in Qatar develop problem-solving skills?
12.How can families in Qatar create number-rich environments to improve Factors of 364 skills?
Glossaries for Factors of 550
Factors: Numbers that can divide another number completely without leaving a remainder.
For example, 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364 are factors of 364.
Negative Factors: The negative counterparts of positive factors. For 364, they are -1, -2, -4, -7, -13, -14, -26, -28, -52, -91, -182, and -364.
Prime Factors: Prime numbers that, when multiplied together, yield the original number. For 364, the prime factors are 2, 7, and 13.
Prime Factorization: The process of expressing a number as a product of its prime factors. For 364, the prime factorization is 2² × 7 × 13.
Multiple: The result of multiplying a number by an integer. For example, 364 is a multiple of 13 because 13 × 28 = 364.
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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.
