Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To divide the pens equally, we need to divide the total pens by the number of boxes.
518/37 = 14
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.
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.
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.
To find the number of stacks, divide the total number of boxes by the number of boxes in each stack.
518/2 = 259
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.
Dividing the participants by the total number of teams, we get the number of participants in each team.
518/7 = 74
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.
Divide the total books by the number of shelves.
518/2 = 259
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.
: She loves to read number jokes and games.