209 LearnersLast updated on May 26th, 2025
Factors of 455
Factors of 455 are numbers that can divide 455 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 455 and the different methods to find them.
What are the Factors of 455?
The factors of 455 are the numbers that divide 455 evenly.
Positive Factors: These are the positive numbers that divide 455 evenly.
Positive factors are 1, 5, 7, 13, 35, 65, 91, and 455.
Negative Factors: These are negative counterparts of the positive factors.
Negative factors are -1, -5, -7, -13, -35, -65, -91, -455
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 455 as the product.
Prime factors: 5, 7, 13
Prime Factorization: Prime factorization involves breaking 455 into its prime factors.
It is expressed as 5 × 7 × 13
Table listing the factors of 455
|
Positive Factors |
1, 5, 7, 13, 35, 65, 91, 455 |
|
Negative Factors |
-1, -5, -7, -13, -35, -65, -91, -455 |
|
Prime Factors |
5, 7, 13 |
|
Prime Factorization |
51 × 71 × 131 |
This breakdown helps in understanding the various factors of 455, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 455?
Finding the factors of a number consists of various methods, such as:
Methods to find the factors of 455:
- 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 455 as their product.
Step 1: Find the pair of numbers whose product is 455.
Step 2: The factors are those numbers, when multiplied, give 455.
Step 3: Make a list of numbers whose product will be 455.
A list of numbers whose products are 455 is given below:
- 1 × 455 = 455
- 5 × 91 = 455
- 7 × 65 = 455
- 13 × 35 = 455
Thus, the factors of 455 are 1, 5, 7, 13, 35, 65, 91, and 455.
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: 455 ÷ 1 = 455
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 455 are 1, 5, 7, 13, 35, 65, 91, and 455
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 455: Number 455 has only three prime factors.
Prime factors of 455: 5, 7, 13
To find the prime factors of 455, we can divide 455 with the prime numbers like 5, 7, and 13 from the list of factors of 455.
Step 1: Divide 455 with the prime number 5. 455 ÷ 5 = 91
Step 2: Divide 91 with the prime number 7. 91 ÷ 7 = 13
Step 3: Divide 13 with the prime number 13. 13 ÷ 13 = 1
Prime Factorization of 455: Prime Factorization breaks down the prime factors of 455.
Expressed as 51 × 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 455 into its prime factors: 5 × 7 × 13
Positive and Negative Factor Pairs of 455
Factors of 455 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, 455), (5, 91), (7, 65), (13, 35)
Negative Factor Pairs: (-1, -455), (-5, -91), (-7, -65), (-13, -35)
Common Mistakes and How to Avoid Them in Factors of 455
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 455.
Since numbers ending in 5 are divisible by 5, you can think that 5 is the only factor of 455. Remember that factors are numbers that can divide the given number equally. So, other numbers that can divide 455 completely are 1, 7, 13, 35, 65, 91, and 455.
Solved Examples for Factors of 455
Problem 1
Can you check whether 15 and 45 are co-prime?
No, 15 and 45 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 15: 1, 3, 5, 15
Factors of 45: 1, 3, 5, 9, 15, 45
Here, the GCF is 15. So, 15 and 45 are not co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 455 is a multiple of 5
Yes, 455 is a multiple of 5
Explanation
A multiple of 5 is any number that ends in 0 or 5. Here 455 does end in 5 thus becomes a multiple of 5
Problem 3
Identify the perfect square from the factors of 455
The perfect square factor of 455 is 1
Explanation
From the factors of 455, the numbers that can be multiplied twice to get the product of another integer are the perfect squares. The only perfect square factor of 455 is 1 (1 × 1).
Problem 4
What are the factors of 455?
The factors of 455 are 1, 5, 7, 11, 35, 55, 77, and 455
Explanation
To find the factors of 455, divide it by all numbers from 1 to 455 and see which numbers divide it evenly without leaving a remainder. The numbers that meet this criterion are its factors.
Problem 5
Are 7 and 455 co-prime?
No, 7 and 455 are not co-prime
Explanation
To determine if two numbers are co-prime, list their factors and find the GCF. If the GCF is greater than 1, they are not co-prime.
Factors of 7: 1, 7
Factors of 455: 1, 5, 7, 11, 35, 55, 77, 455
Here, the GCF is 7. So, 7 and 455 are not co-prime. For numbers to be co-prime, their GCF should be 1.
FAQ’s for Factors of 455
1.What are the factors of 455?
2.How do you determine if a number is a factor of 455?
3.What is the smallest factor of 455?
4.What is the largest factor of 455?
5.How many factors does 455 have?
6.How many odd factors does 455 have?
7.What factors go into 455?
8.Do any perfect squares exist in the factors of 455?
Glossaries for Factors of 329
- Factors: Numbers that can divide a given number completely without leaving a remainder.
- Prime Factors: Prime numbers that, when multiplied together, yield the given number as their product.
- Prime Factorization: The process of breaking down a number into its prime factors and expressing it as a product of prime numbers.
- Multiple: Numbers are obtained when another number is multiplied by an integer.
- Perfect Square: When a number is multiplied twice, the resulting product will be an integer and will not have any decimal units.
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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.
