127 LearnersLast updated on May 26th, 2025
Factors of 518
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 518, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 518?
The numbers that divide 518 evenly are known as factors of 518.
A factor of 518 is a number that divides the number without remainder.
The factors of 518 are 1, 2, 7, 37, 74, 259, and 518.
Negative factors of 518: -1, -2, -7, -37, -74, -259, and -518.
Prime factors of 518: 2, 7, and 37.
Prime factorization of 518: 2 × 7 × 37.
The sum of factors of 518: 1 + 2 + 7 + 37 + 74 + 259 + 518 = 898
How to Find Factors of 518?
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 518. Identifying the numbers which are multiplied to get the number 518 is the multiplication method.
Step 1: Multiply 518 by 1, 518 × 1 = 518.
Step 2: Check for other numbers that give 518 after multiplying
2 × 259 = 518
7 × 74 = 518
37 × 14 = 518
Therefore, the positive factor pairs of 518 are: (1, 518), (2, 259), (7, 74), (37, 14).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with 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 518 by 1, 518 ÷ 1 = 518.
Step 2: Continue dividing 518 by the numbers until the remainder becomes 0.
518 ÷ 1 = 518
518 ÷ 2 = 259
518 ÷ 7 = 74
518 ÷ 37 = 14
Therefore, the factors of 518 are: 1, 2, 7, 37, 74, 259, and 518.
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 518 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
518 ÷ 2 = 259
259 ÷ 7 = 37
37 is a prime number, so it cannot be divided further.
The prime factors of 518 are 2, 7, and 37.
The prime factorization of 518 is: 2 × 7 × 37.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 518 is divided by 2 to get 259.
Step 2: Now divide 259 by 7 to get 37. 37 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 518 is: 2 × 7 × 37.
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 518: (1, 518), (2, 259), (7, 74), and (37, 14).
Negative factor pairs of 518: (-1, -518), (-2, -259), (-7, -74), and (-37, -14).
Common Mistakes and How to Avoid Them in Factors of 518
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 518, 1 and 518 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, The factors of 518 consist of -1, -2, -7, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 518/1.5 = 345.333, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes. For example, thinking all the factors of 518 are prime numbers.
For example, 2, 7, and 37 are the prime factors of 518, but it has other factors like 74, 14.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 518 as 2 × 7 × 37 and missing all the key factors.
Factors of 518 Examples
Problem 1
A company has 518 pens and wants to distribute them equally into 37 boxes. How many pens will each box have?
Each box will have 14 pens.
Explanation
To divide the pens equally, we need to divide the total pens by the number of boxes.
518/37 = 14
Problem 2
A rectangular plot has a length of 74 meters and a total area of 518 square meters. What is the width of the plot?
7 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
518 = 74 × width
To find the value of width, we need to divide 518 by 74.
518/74 = width
Width = 7.
Problem 3
A warehouse contains 518 boxes and wants to arrange them in stacks of 2. How many stacks will there be?
There will be 259 stacks.
Explanation
To find the number of stacks, divide the total number of boxes by the number of boxes in each stack.
518/2 = 259
Problem 4
In a tournament, there are 518 participants divided into 7 teams. How many participants are there in each team?
There are 74 participants in each team.
Explanation
Dividing the participants by the total number of teams, we get the number of participants in each team.
518/7 = 74
Problem 5
A library has 518 books to be arranged equally on 2 shelves. How many books will go on each shelf?
Each shelf will have 259 books.
Explanation
Divide the total books by the number of shelves.
518/2 = 259
FAQs on Factors of 518
1.What are the factors of 518?
2.Mention the prime factors of 518.
3.Is 518 a multiple of 7?
4.Mention the factor pairs of 518?
5.What is the square of 518?
6.How can children in India use numbers in everyday life to understand Factors of 518?
7.What are some fun ways kids in India can practice Factors of 518 with numbers?
8.What role do numbers and Factors of 518 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 518 skills?
Important Glossaries for Factors of 518
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 518 are 1, 2, 7, 37, 74, 259, and 518.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 37 are prime factors of 518.
- 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 518 are (1, 518), (2, 259), etc.
- Prime factorization: The process of breaking down a number into its prime components. For example, the prime factorization of 518 is 2 × 7 × 37.
- Negative factors: Factors that are negative, which when multiplied together also give the original number. For example, negative factors of 518 are -1, -2, -7, -37, -74, -259, and -518.
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About BrightChamps in India
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.
