202 LearnersLast updated on May 26th, 2025
Factors of 368
Factors of 368 are numbers that can divide 368 completely without a 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 368 and the different methods to find them.
What are the Factors of 368
The factors of 368 are the numbers that divide 368 evenly.
Positive Factors: These are the positive numbers that divide 368 evenly.
Positive factors are 1, 2, 4, 8, 16, 23, 46, 92, 184, and 368.
Negative Factors: These are negative counterparts of the positive factors.
Negative factors are -1, -2, -4, -8,-16, -23, -46, -92, -184, -368
Prime Factors: Prime factors are the prime numbers themselves, which, when multiplied together, give 368 as the product.
Prime factors: 2, 46
Prime Factorization: Prime factorization involves breaking 368 into its prime factors.
It is expressed as 24 × 23
Table listing the factors of 368
|
Positive Factors |
1, 2, 4, 8, 16, 23, 46, 92, 184, 368 |
|
Negative Factors |
-1, -2, -4, -8, - 16, -23, -46, -92, -184, -368 |
|
Prime Factors |
2, 23 |
|
Prime Factorization |
24 × 23 |
This breakdown helps in understanding the various factors of 368, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 368?
There are different methods to find the factors of 368.
Methods to find the factors of 368:
- 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 368 as their product.
Step 1: Find the pair of numbers whose product is 368.
Step 2: The factors are those numbers which, when multiplied, give 368.
Step 3: Make a list of numbers whose product will be 368.
A list of numbers whose products are 368 is given below:
- 1 × 368 = 368
- 2 × 184 = 368
- 4 × 92 = 368
- 8 × 46 = 368
Thus, the factors of 368 are 1, 2, 4, 8, 46, 92, 184, and 368.
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: 368 ÷ 1 = 368
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 368 are 1, 2, 4, 8, 16, 23, 46, 92, 184, and 368.
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 368: The number 368 has two prime factors.
Prime factors of 368: 2, 23
To find the prime factors of 368, we can divide 368 with the prime numbers from the list of factors of 368.
Step 1: Divide 368 with the prime number 2 368 ÷ 2 = 184
Step 2: Divide 184 with the prime number 2 184 ÷ 2 = 92
Step 3: Continue dividing by 2 until it cannot be divided further. 92 ÷ 2 = 46 46 ÷ 2 = 23 (23 is a prime number)
Prime Factorization of 368: Prime Factorization breaks down the prime factors of 368.
Expressed as 24 × 23
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 368 into its prime factors: 2 × 23
Positive and Negative Factor Pairs of 368
Factors of 368 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, 368), (2, 184), (4, 92), (8, 46)
Negative Factor Pairs: (-1, -368), (-2, -184), (-4, -92), (-8, -46)
Common Mistakes and How to Avoid Them in Factors of 368
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 as the only factor of 368.
Since 368 is even, it is divisible by 2. However, other numbers such as 1, 4, 8, 16, 23, 46, 92, 184, and 368 also divide it completely. Remember that factors are numbers that can divide the given number equally.
Factors of 368 Examples
Problem 1
Can you identify whether 16 and 368 are co-prime?
No, 16 and 368 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 16: 1, 2, 4, 8, 16
Factors of 368: 1, 2, 4, 8, 16, 23, 46, 92, 184, 368
Here, the GCF is 8. So 16 and 368 are not co-prime.
For co-prime numbers, the GCF should be 1.
Problem 2
Verify whether 368 is a multiple of 9.
No, 368 is not a multiple of 9.
Explanation
Multiples of 9 are numbers we get when 9 is multiplied by another number.
No integer can be multiplied by 9 to get 368 as the product.
Problem 3
Identify the perfect square from the factors of 368.
The perfect square factor of 368 is 4, and its 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.
Problem 4
Is 368 divisible by 23?
Yes, 368 is divisible by 23.
Explanation
To check divisibility, divide 368 by 23.
368 ÷ 23 = 16 (an integer).
So, 368 is divisible by 23.
Problem 5
What is the largest factor of 368 other than 368 itself?
The largest factor of 368 other than itself is 184.
Explanation
Factors of 368 are 1, 2, 4, 8, 16, 23, 46, 92, 184, 368.
The largest factor other than 368 is 184.
FAQs on Factors of 368
1.What are the factors of 368?
2.How do you determine if a number is a factor of 368?
3.What is the smallest factor of 368?
4.What is the largest factor of 368?
5.How many factors does 368 have?
6.How many odd factors does 368 have?
7.What factors go into 368?
8.Do any perfect squares exist in the factors of 368?
Important glossaries for the Factors of 368
- Factor: A number that divides another number completely without leaving a remainder.
- Negative Factors: Negative counterparts of positive factors, which also divide the number completely.
- Prime Factors: Prime numbers that, when multiplied together, produce the given number.
- Prime Factorization: The process of expressing a number as a product of its prime factors.
- Perfect Square: A factor that is the square of an integer.
Explore More numbers
Previous to Factors of 368
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.
