164 LearnersLast updated on May 26th, 2025
Factors of 457
Factors of 457 are numbers that can divide 457 completely without any remainder. We often use factors in activities like organizing events and seating arrangements in our daily lives. In this topic, we will learn more about the factors of 457 and the different methods to find them.
What are the Factors of 457?
The factors of 457 are 1 and 457.
Positive factors: These are the numbers that can divide 457 without leaving a remainder.
Positive factors: 1, 457
Negative factors: These are the negative counterparts of the positive factors.
Negative factors: -1, -457
Prime Factors: Prime factors are the prime numbers themselves that, when multiplied together, give 457 as the product.
Prime factors: 457 (since 457 is a prime number, it is only divisible by 1 and itself)
Prime Factorization: Prime factorization involves breaking 457 into its prime factors. Since 457 is prime, its prime factorization is simply:
Prime factorization: 457
How to Find the Factors of 457?
There are different methods to find the factors of 457.
Methods to find the factors of 457:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree (not applicable for prime numbers)
Finding Factors Using Multiplication
The multiplication method finds the pair of factors that give 457 as their product.
Step 1: Find the pair of numbers whose product is 457.
1 × 457 = 457
Thus, the factors of 457 are 1 and 457.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number.
Step 1: Since every number is divisible by 1, 1 will always be a factor.
Example: 457 ÷ 1 = 457.
Step 2: Move to the next integer and test divisibility. 457 is only divisible by 1 and 457 itself.
Thus, the factors of 457 are 1 and 457.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number simplified using its prime factors and expressed in the form of prime factors is its prime factorization.
Prime Factors of 457: Since 457 is a prime number, it only has two prime factors, 1 and 457.
Prime Factorization of 457: Since 457 is prime, its prime factorization is simply:
Expressed as 457
Factor Tree
The prime factorization of 457 is visually represented using a factor tree, though it is simple for prime numbers. Since 457 has no other factors besides 1 and itself, the factor tree is minimal:
457 (as a standalone prime factor)
Factors of 457 can be written in both positive and negative pairs. They are like team members whose product will be equal to the number given.
Positive Factor Pairs: (1, 457)
Negative Factor Pairs: (-1, -457)
Common Mistakes and How to Avoid Them in Factors of 457
Mistakes can occur while finding the factors. Here are some common errors and how to avoid them:
Mistake 1
Assuming that 457 has more factors.
457 is a prime number, meaning it only has two factors: 1 and itself. Ensure you check the divisibility carefully to avoid assuming there are additional factors.
Factors of 457 Examples
Problem 1
Can you check whether 75 and 457 are co-prime?
Yes, 75 and 457 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 75: 1, 3, 5, 15, 25, 75
Factors of 457: 1, 457
Here, the GCF is 1. So, 75 and 457 are co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 457 is a multiple of 3
No, 457 is not a multiple of 3
Explanation
Multiples of 3 are numbers we get when 3 is multiplied by another number. No integer multiplied by 3 results in 457 as a product.
Problem 3
Identify the perfect square from the factors of 457
The perfect square factor of 457 is 1 and the root is 1
Explanation
A perfect square is a number we get when the same number is multiplied twice. The only perfect square in the factors of 457 is 1 (1 × 1).
Problem 4
Check if 457 is a prime number
Yes, 457 is a prime number
Explanation
A prime number has only two factors: 1 and itself. The only factors of 457 are 1 and 457, so it is prime.
Problem 5
Determine if 457 is divisible by 5
No, 457 is not divisible by 5
Explanation
A number is divisible by 5 if its last digit is 0 or 5. The last digit of 457 is 7, so it is not divisible by 5.
FAQs on Factors of 457
1.What are the factors of 457?
2.How do you determine if a number is a factor of 457?
3.What is the smallest factor of 457?
4.What is the largest factor of 457?
5.How many factors does 457 have?
6.How many odd factors does 457 have?
7.What factors go into 457?
Important glossaries for the Factors of 457
- Factors: Numbers that can divide another number completely without leaving a remainder.
- Prime Factors: Prime numbers that, when multiplied together, result in a given number.
- Prime Factorization: The process of expressing a number as a product of its prime factors.
- Perfect Square: A number that results from multiplying a number by itself.
- Multiple: The product of a given number and 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.
