124 LearnersLast updated on May 26th, 2025
Factors of 508
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 508, how they are used in real life, and tips to learn them quickly.
What are the Factors of 508?
The numbers that divide 508 evenly are known as factors of 508.
A factor of 508 is a number that divides the number without remainder.
The factors of 508 are 1, 2, 4, 127, 254, and 508.
Negative factors of 508: -1, -2, -4, -127, -254, and -508.
Prime factors of 508: 2 and 127.
Prime factorization of 508: 2² × 127.
The sum of factors of 508: 1 + 2 + 4 + 127 + 254 + 508 = 896
How to Find Factors of 508?
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 508. Identifying the numbers which are multiplied to get the number 508 is the multiplication method.
Step 1: Multiply 508 by 1, 508 × 1 = 508.
Step 2: Check for other numbers that give 508 after multiplying
2 × 254 = 508
4 × 127 = 508
Therefore, the positive factor pairs of 508 are: (1, 508), (2, 254), and (4, 127).
All these factor pairs result in 508.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 508 by 1, 508 ÷ 1 = 508.
Step 2: Continue dividing 508 by the numbers until the remainder becomes 0.
508 ÷ 1 = 508
508 ÷ 2 = 254
508 ÷ 4 = 127
Therefore, the factors of 508 are: 1, 2, 4, 127, 254, 508.
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 508 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
508 ÷ 2 = 254
254 ÷ 2 = 127
127 ÷ 127 = 1
The prime factors of 508 are 2 and 127.
The prime factorization of 508 is: 2² × 127.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 508 is divided by 2 to get 254.
Step 2: Now divide 254 by 2 to get 127.
Step 3: 127 is a prime number, that cannot be divided anymore.
So, the prime factorization of 508 is: 2² × 127.
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 508: (1, 508), (2, 254), and (4, 127).
Negative factor pairs of 508: (-1, -508), (-2, -254), and (-4, -127).
Common Mistakes and How to Avoid Them in Factors of 508
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 508, 1 and 508 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 508 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 508/1.5 = 338.666…, 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 508 are prime numbers.
For example, 2 and 127 are the prime factors of 508, but it has other factors like 4, 254.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 508 as 2² × 127 and missing all the key factors.
Factors of 508 Examples
Problem 1
There are 4 teams and 508 points. How will they distribute the points equally among the teams?
They will get 127 points each.
Explanation
To distribute the points equally, we need to divide the total points by the number of teams.
508/4 = 127
Problem 2
A rectangular garden has a width of 4 meters and a total area of 508 square meters. Find the length.
127 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
508 = length × 4
To find the value of the length, we need to divide 508 by 4.
508/4 = length
Length = 127.
Problem 3
There are 127 packages and 508 items. How many items will be in each package?
Each package will have 4 items.
Explanation
To find the items in each package, divide the total items by the number of packages.
508/127 = 4
Problem 4
In a class, there are 508 books, and 2 shelves. How many books are there on each shelf?
There are 254 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
508/2 = 254
Problem 5
508 toys need to be packed into 127 boxes. How many toys will go into each box?
Each box will have 4 toys.
Explanation
Divide total toys by the number of boxes.
508/127 = 4
FAQs on Factors of 508
1.What are the factors of 508?
2.Mention the prime factors of 508.
3.Is 508 a multiple of 2?
4.Mention the factor pairs of 508?
5.What is the square of 508?
Important Glossaries for Factors of 508
- Factors: The numbers that divide a given number without leaving a remainder are called factors. For example, the factors of 508 are 1, 2, 4, 127, 254, and 508.
- Prime factors: The factors which are prime numbers. For example, 2 and 127 are prime factors of 508.
- 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 508 are (1, 508), (2, 254), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 508 is 2² × 127.
- Multiple: A number that can be expressed as the product of another number and an integer. For example, 508 is a multiple of 2.
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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.
