162 LearnersLast updated on May 26th, 2025
Factors of 465
Factors of 465 are numbers that can divide 465 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 465 and the different methods to find them.
What are the Factors of 465?
The factors of 465 are the numbers that divide 465 evenly.
Positive Factors: These are the positive numbers that divide 465 evenly.
Positive factors are 1, 3, 5, 7, 9, 15, 31, 45, 65, 93, 155, and 465.
Negative Factors: These are negative counterparts of the positive factors. Negative factors: -1, -3, -5, -7, -9, -15, -31, -45, -65, -93, -155, -465.
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 465 as the product. Prime factors: 3, 5, 31.
Prime Factorization: Prime factorization involves breaking 465 into its prime factors. It is expressed as 3 × 5 × 7.
Table listing the factors of 465
|
Positive Factors |
1, 3, 5, 7, 9, 15, 31, 45, 65, 93, 155, 465 |
|
Negative Factors |
-1, -3, -5, -7, -9, -15, -31, -45, -65, -93, -155, -465 |
|
Prime Factors |
3 5 31 |
|
Prime Factorization |
3 × 5 × 31 |
This breakdown helps in understanding the various factors of 465, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 465?
Finding the factors of 465, we can make use of various methods. The methods are listed below.
Methods to find the factors of 465:
- 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 465 as their product.
Step 1: Find the pair of numbers whose product is 465.
Step 2: The factors are those numbers, when multiplied, give 465.
Step 3: Make a list of numbers whose product will be 465.
A list of numbers whose products are 465 is given below:
- 1 × 465 = 465
- 3 × 155 = 465
- 5 × 93 = 465
- 7 × 65 = 465
- 9 × 45 = 465
- 15 × 31 = 465
Thus, the factors of 465 are 1, 3, 5, 7, 9, 15, 31, 45, 65, 93, 155, and 465.
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: 465 ÷ 1 = 465
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 465 are 1, 3, 5, 7, 9, 15, 31, 45, 65, 93, 155, and 465.
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 465: Number 465 has three prime factors.
Prime factors of 465: 3, 5, 31
To find the prime factors of 465, we can divide 465 with the prime numbers like 3, 5, and 31 from the list of factors of 465.
Step 1: Divide 465 with the prime number 3
- 465 ÷ 3 = 155
Step 2: Divide 155 with the prime number 5
- 155 ÷ 5 = 31
Step 3: Divide 31 with the prime number 7
- 31 ÷ 31 = 1
Prime Factorization of 465: Prime Factorization breaks down the prime factors of 465.
Expressed as 3 × 5 × 31
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 465 into its prime factors: 3 × 5 × 31
Positive and Negative Factor Pairs of 465
Factors of 465 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, 465), (3, 155), (5, 93), (7, 65), (9, 45), (15, 31)
Negative Factor Pairs: (-1, -465), (-3, -155), (-5, -93), (-7, -65), (-9, -45), (-15, -31)
Common Mistakes and How to Avoid Them in Factors of 465
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 5 as the only factor of 465
Since numbers ending in 5 are divisible by 5, you might think 5 is the only factor of 465. Remember that factors are numbers that can divide the given number equally. So, other numbers that can divide 465 completely are 1, 3, 7, 9, 15, 31, 45, 65, 93, 155, and 465.
Factors of 379 Examples
Problem 1
Can you check whether 75 and 25 are co-prime?
No, 75 and 25 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 75: 1, 3, 5, 15, 25, 75
Factors of 25: 1, 5, 25
Here, the GCF is 25. So, 75 and 25 are not co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 75 is a multiple of 7
No, 75 is not a multiple of 7
Explanation
Multiples of 7 are numbers we get when 7 is multiplied by another number. No number can be multiplied by 7 to get 75 as the product.
Problem 3
Identify the perfect square from the factors of 75
The perfect square factor of 75 is 25 and the root is 5
Explanation
A perfect square is a number we get when the same number is multiplied twice. When 5 is multiplied twice (5×5) we get the perfect square 25.
Problem 4
Find the factors of 465
The factors of 465 are 1, 3, 5, 7, 15, 31, 45, 93, 155, 465
Explanation
To find the factors of a number, list all the numbers that divide the number without leaving a remainder. Here, the factors of 465 are 1, 3, 5, 7, 15, 31, 45, 93, 155, and 465.
Problem 5
Identify the largest factor of 465
The largest factor of 465 is 465
Explanation
The largest factor of any number is the number itself. Hence, the largest factor of 465 is 465.
FAQs on Factors of 465
1.What are the factors of 465?
2.How do you determine if a number is a factor of 465?
3.What is the smallest factor of 465?
4.What is the largest factor of 465?
5.How many factors does 465 have?
6.How many odd factors does 465 have?
7.What factors go into 465?
8.Do any perfect squares exist in the factors of 465?
Important glossaries for the Factors of 465
- Factors: Numbers that can divide a given number completely without leaving a remainder. Example: The factors of 379 are 1 and 379.
- Prime Factors: Prime numbers from the list of factors of a particular number, when multiplied together, give the original number. Since 379 is a prime number, its prime factors are just 379 itself.
- Prime Factorization: The process of breaking down a number into its prime factors. The prime factorization of 379 is simply 379.
- Multiple: A number that is the product of a given number and another integer. For example, multiples of 7 are 7, 14, 21, etc.
- Perfect Square: A number that is the product of an integer multiplied by itself. For example, 25 is a perfect square because 5 × 5 = 25.
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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.
