135 LearnersLast updated on May 29th, 2025
Factors of 463
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 463, how they are used in real life, and tips to learn them quickly.
What are the Factors of 463?
The number that divides 463 evenly is known as a factor of 463.
A factor of 463 is a number that divides the number without a remainder.
The factors of 463 are 1 and 463, because 463 is a prime number.
Negative factors of 463: -1 and -463.
Prime factors of 463: 463.
Prime factorization of 463: 463.
The sum of factors of 463: 1 + 463 = 464
How to Find Factors of 463?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify pairs of numbers that are multiplied to give 463. Since 463 is a prime number, it only has trivial multiplication factors:
Step 1: Multiply 463 by 1, 463 × 1 = 463.
Therefore, the positive factor pairs of 463 are: (1, 463).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number by whole numbers until the remainder becomes zero and listing out the numbers that result in whole numbers as factors. Since 463 is a prime number, it only divides evenly by 1 and itself:
Step 1: Divide 463 by 1, 463 ÷ 1 = 463.
Step 2: Try dividing 463 by other numbers, but they will not divide evenly.
Therefore, the factors of 463 are: 1 and 463.
Prime Factors and Prime Factorization
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, because 463 is a prime number, it cannot be broken down further.
The prime factor of 463 is 463 itself.
The prime factorization of 463 is: 463.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. However, since 463 is a prime number, it cannot be broken down further using a factor tree. The prime factorization of 463 is: 463.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 463: (1, 463).
Negative factor pairs of 463: (-1, -463).
Common Mistakes and How to Avoid Them in Factors of 463
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
People might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 463, 1 and 463 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 463 consist of -1 and -463.
Mistake 3
Including the Fraction
Sometimes, one might mistakenly consider fractions as factors. Only whole numbers can be factors.
For example, thinking 463/2 = 231.5 as a factor is incorrect because it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes. For example, thinking the factors of 463 are all prime numbers.
For instance, 463 is a prime number, but not all factors are necessarily prime unless the number itself is prime.
Mistake 5
Mistake in Factorization
One might skip steps in factorization and end up writing incorrect factors.
For example, not recognizing that 463 is a prime and trying to break it down further unnecessarily.
Factors of 463 Examples
Problem 1
A charity has 463 books and wants to distribute them equally among 1 school. How many books will each school receive?
Each school will receive 463 books.
Explanation
To divide the books equally, we divide the total number of books by the number of schools.
463/1
= 463
Problem 2
An art gallery has 463 paintings and wants to hang them in 1 row. How many paintings will be in each row?
There will be 463 paintings in each row.
Explanation
To find the number of paintings in each row, divide the total number of paintings by the number of rows.
463/1
= 463
Problem 3
A team has 463 points and wants to distribute them equally among 1 player. How many points will each player receive?
Each player will receive 463 points.
Explanation
To divide the points equally, divide the total points by the number of players.
463/1
= 463
Problem 4
A library has 463 books, and they want to place them on 1 shelf. How many books will be on each shelf?
There will be 463 books on each shelf.
Explanation
To find the number of books on each shelf, divide the total books by the number of shelves.
463/1
= 463
Problem 5
A school has 463 students participating in a single event. How many students will attend the event?
All 463 students will attend the event.
Explanation
All students are participating, so the total number attending is the total number of students.
463/1
= 463
FAQs on Factors of 463
1.What are the factors of 463?
2.Mention the prime factor of 463.
3.Is 463 a multiple of 2?
4.Mention the factor pairs of 463?
5.What is the square of 463?
Important Glossaries for Factors of 463
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 463 are 1 and 463.
- Prime factors: The factors which are prime numbers. For example, 463 is a prime factor of itself.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 463 is (1, 463).
- Prime number: A number greater than 1 that has no divisors other than 1 and itself. For example, 463 is a prime number.
- Multiplication: The mathematical operation to find the product of two numbers. For example, 1 × 463 = 463.
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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.
