# What is the Factor of 18 and How Does it Work?

SECTIONS

What is the factor of 18, and how does its work? If you are looking for a details guide about the factor of 18, how to find a factor of 18 by prime factorization, the division method, and how we can divide it into positive and negative factors, then go through this article. Here we discuss all these points in detail.

Before diving into details and finding all the factors of 18, let’s discuss what the word factor means and the different methods to calculate it.

## Introduction to Factors

Factors play a crucial role in mathematics. If you divide a given number with no remainder left, the divisor is called a factor of a given number. So, factors build a strong relationship between different numbers and solve mathematical problems such as factorization of the quadratic equation.

In this article, we will delve into the concept of factors and explore the specific case of the factor of 18.

## Understanding the Concept of Factors

Before diving into the factor of 18, let’s clearly understand what factors are.

Factors are the numbers that divide a given number without leaving a remainder. For instance, the factors 12 are 1, 2, 3, 4, 6, and 12. Here we multiply the pairs of numbers from factors and get the original number.

## What is the Factor of 18? How to find it?

The factor of a number refers to the numbers that divide it evenly without leaving a remainder. What is the factor of 18? In the case of 18, the factor of 18 would be the set of numbers that divide 18 without any remainder. Factors of any number can be positive or negative if they satisfy the evenly dividing condition.

There are two methods to find the factors.

1. By prime Factorization
2. By divisions

Let’s discuss both of them in detail.

### Factors of 18 by division method

To determine what is the factor of 18, we need to consider all the numbers that divide 18 without leaving a remainder. So, factors of any number lie between 1 and that number. So, the positive factors of 18 will be between 1 and 18. Now check all the numbers from 1 to 18 and determine which numbers divide 18.

##### Factor or not
118/1 =181 exactly divide 18.  1 is a factor of 18.
218/2=92 exactly divide 18.  2 is a factor of 18.
318/3=63 exactly divided 18.  3 is a factor of 18.
418/4= 4 with 2 remainder4 does not exactly divide 18.  4 is not a factor of 18.
518/5 =3 with 3 remainder5 does not exactly divide 18.  5 is not a factor of 18.
618/6=36 exactly divides 18.  6 is a factor of 18.
718/7 =2 with 4 remainder7 does not exactly divide 18.  7 is not a factor of 18.
818/8 =2 with 2 remainder8 does not exactly divide 18.  8 is not a factor of 18.
918/9=29 exactly divides 18.  9 is a factor of 18.
1018/10 =1 with 8 remainder10 does not exactly divide 18.  10 is not a factor of 18.
1118/11 =1 with 7 remainder11 does not exactly divide 18.  11 is not a factor of 18.
1218/12 =1 with 6 remainder12 does not exactly divide 18.  12 is not a factor of 18.
1318/13 =1 with 5 remainder13 does not exactly divide 18.  13 is not a factor of 18.
1418/14 =1 with 4 remainder14 does not exactly divide 18.  14 is not a factor of 18.
1518/15 =1 with 3 remainder15 does not exactly divide 18.  15 is not a factor of 18.
1618/16 =1 with 2 remainder16 does not exactly divide 18.  16 is not a factor of 18.
1718/17 =1 with 1 remainder17 does not exactly divide 18.  17 is not a factor of 18.
1818/18=118 exactly divides 18.  18 is a factor of 18.

From this table, its clears that 18 has 1, 2, 3, 6, 9, and 18 as its factors. These numbers can be multiplied in various combinations to obtain the number 18.

### How to find factor of 18 by Prime Factorization method

Prime factorization is the process of expressing a number as a product of prime numbers. To find what is the factor of 18 by prime factorization, we need to determine the numbers that, when multiplied together, result in 18. In the case of 18, the prime factorization is 2 × 3 × 3.

## Prime factor of 18

As 18 have the factors, 1,2,3,6,9,,18. Now check which of them are the prime factors.

## Common Factors of 18

The common factors of a set of numbers are the factors that are shared by all the numbers in the set. In the case of 18, let’s consider another number, say 36.

And 36  has the following factors.

So, from these examples, it’s clear that 18 and 36 have 1, 2, 3, 6, 9, and 18 as common factors.

## Negative Factors of 18

Negative factors of 18 are all the additive inverse of the positive numbers. As positive factors are the 1,2,3,6,9 and 18. So, negative factors 18 are -1,-2,-3,-6,-9, and -18.

## Factors pairs of 18

Factor pairs of 18 are the number that multiplies together, giving us 18. Here are all the factors pairs of 18.

Positive factors pair                                        Negative factors pairs

1,18                                                                      -1,-18

2,9                                                                          -2,-9

3,6                                                                          -3,-6

## Applications of Factors in Mathematics

Mathematicians use factors in various applications. They are especially crucial in number theory because they enable us to comprehend the distinctive features of numbers. Prime factorization, determining the greatest common factor, and equation solving all include factors. Factors are also important in geometry, where they aid in calculating areas, volumes, and shape dimensions.

## Real-Life Examples of Factors

Factors are not just used in theoretical mathematics; they can also be used in real-world situations. Let’s imagine that we need to split objects into equally sized groups. Various factors affect how many groups we can form. For instance, if we have 18 cookies and want to distribute them evenly among a group of friends, we can calculate the potential number of friends by multiplying 18 by the numbers 1, 2, 3, 6, and 18.

## Conclusion

Factors are a crucial idea in mathematics, to sum up. They assist us in comprehending the connections and features of numbers. A number’s factor is the set of numbers that divide it in two equally without producing a remainder. What is the factor of 18? Factors of 18 included 1, 2, 3, 6, 9, and 18. We can use prime factorization to represent a number as the product of prime numbers. Factors are used in many areas of mathematics and can also be observed in real-world situations. We learn more about the universe of numbers and how they are connected through comprehending factors.

Stay tuned with our latest math posts