121 LearnersLast updated on May 26th, 2025
Factors of 460
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 460, how they are used in real life, and tips to learn them quickly.
What are the Factors of 460?
The numbers that divide 460 evenly are known as factors of 460.
A factor of 460 is a number that divides the number without remainder.
The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, and 460.
Negative factors of 460: -1, -2, -4, -5, -10, -20, -23, -46, -92, -115, -230, and -460.
Prime factors of 460: 2, 5, and 23.
Prime factorization of 460: 2 × 2 × 5 × 23.
The sum of factors of 460: 1 + 2 + 4 + 5 + 10 + 20 + 23 + 46 + 92 + 115 + 230 + 460 = 1008
How to Find Factors of 460?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 460. Identifying the numbers that are multiplied to get the number 460 is the multiplication method.
Step 1: Multiply 460 by 1, 460 × 1 = 460.
Step 2: Check for other numbers that give 460 after multiplying
2 × 230 = 460
4 × 115 = 460
5 × 92 = 460
10 × 46 = 460
20 × 23 = 460
Therefore, the positive factor pairs of 460 are: (1, 460), (2, 230), (4, 115), (5, 92), (10, 46), (20, 23).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers that result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 460 by 1, 460 ÷ 1 = 460.
Step 2: Continue dividing 460 by the numbers until the remainder becomes 0.
460 ÷ 1 = 460
460 ÷ 2 = 230
460 ÷ 4 = 115
460 ÷ 5 = 92
460 ÷ 10 = 46
460 ÷ 20 = 23
Therefore, the factors of 460 are: 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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, prime factors of 460 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
460 ÷ 2 = 230
230 ÷ 2 = 115
115 ÷ 5 = 23
23 ÷ 23 = 1
The prime factors of 460 are 2, 5, and 23.
The prime factorization of 460 is: 2 × 2 × 5 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 460 is divided by 2 to get 230.
Step 2: Now divide 230 by 2 to get 115.
Step 3: Then divide 115 by 5 to get 23.
Step 4: Here, 23 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 460 is: 2 × 2 × 5 × 23.
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 460: (1, 460), (2, 230), (4, 115), (5, 92), (10, 46), (20, 23).
Negative factor pairs of 460: (-1, -460), (-2, -230), (-4, -115), (-5, -92), (-10, -46), (-20, -23).
Common Mistakes and How to Avoid Them in Factors of 460
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
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 460, 1 and 460 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 460 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 460/1.5 = 306.6667, and 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 all the factors of 460 are prime numbers.
For example, 2, 5, and 23 are the prime factors of 460, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 460 as 2 × 2 × 5 × 23 and missing all the key factors.
Factors of 460 Examples
Problem 1
There are 23 students and 460 pencils. How will they divide it equally?
They will get 20 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils with the number of students.
460/23 = 20
Problem 2
A field is rectangular, the length of the field is 23 meters and the total area is 460 square meters. Find the width?
20 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
460 = 23 × width
To find the value of width, we need to shift 23 to the left side.
460/23 = width
Width = 20.
Problem 3
There are 10 boxes and 460 marbles. How many marbles will be in each box?
Each box will have 46 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
460/10 = 46
Problem 4
In a class, there are 460 students, and 20 groups. How many students are there in each group?
There are 23 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
460/20 = 23
Problem 5
460 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 92 books.
Explanation
Divide total books with shelves.
460/5 = 92
FAQs on Factors of 460
1.What are the factors of 460?
2.Mention the prime factors of 460.
3.Is 460 a multiple of 10?
4.Mention the factor pairs of 460?
5.What is the square of 460?
Important Glossaries for Factors of 460
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, and 460.
- Prime factors: The factors that are prime numbers. For example, 2, 5, and 23 are prime factors of 460.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 460 are (1, 460), (2, 230), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 460 is 2 × 2 × 5 × 23.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 460 is a multiple of 10.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 460
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.
