Factors of 18 and How to Determine Them?
Factor in mathematics is a number that is able to divide another number exactly leaving no remainder. In simple words, factors are whole numbers that can divide a number greater than it exactly and evenly without a remainder. Factors are integers and are never fractions or decimals. They can be both positive and negative integers. Only two factors are possible in the case of prime numbers while for composite numbers there are more than two factors.
The factor is an easy but very useful topic. It is such an important mathematical tool that is used in all level maths starting from elementary school level to higher advanced levels. It is used in all other science and many arts subjects also. An important tool for measurements involved in day-to-day life. Similarly, by the term factors of 18, we mean all those integers that can divide the number 18 evenly with a remainder of zero.
Factors of 18
Factors of 18 are the products of such numbers which completely divide the given number 18. Factors of a given number have two values; they can be either positive or negative numbers. By multiplying the factors of a number we get the original number. For example 1, 2, 3, 4, 6, 12 are the factors of 12. Hence we have 4 x 3 = 12 or 6 x 2 = 12 as the pair factors of 12. In this article, we will study the factors of 18, what are the factors of 18, what is the prime factorization of 18, the factor tree of 18, all factors of 18, and examples. Factor pairs of the number 18 are the pairs of the whole numbers which could be either positive or negative but not a fraction or decimal number. Factorisation is the common method to find the factors of 18.
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Definition
The factors of a number are defined as the numbers which give the original number on multiplying the two factors. The factors can be either positive or negative integers. Factors of 18 are all the integers that can evenly divide the given number 18. Now let us study how to calculate all factors of 18.
What are the Factors of 18?
According to the definition of factors of 18, we know that factors of 18 are all the positive or negative integers that divide the number 18 completely. So let us simply divide the number 18 by every number which completely divides 18 in ascending order till 18.
18 ÷ 1 = 18
18 ÷ 2 = 9
18 ÷ 3 = 6
18 ÷ 4 = not divides completely
18 ÷ 5 = not divides completely
18 ÷ 6 = 3
18 ÷ 7 = not divides completely
18 ÷ 8 = not divides completely
18 ÷ 9 = 2
18 ÷18 = 1
So all factors of 18: 1, 2, 3, 6, 9, and 18.
We know that factors also include negative integers hence we can also have,
list of negative factors of 18: -1, -2, -3, -6, -9 and -18.
All Factors of 18 Can be Listed as Follows:
Hence 18 has a total of 6 positive factors and 6 negative factors.
All Factor Pairs of 18
All Factor Pairs of 18 are combinations of two factors that when multiplied together give 18.
List of all the positive pair factors of 18
1 x 18 = 18; pair factors are(1, 18)
3 x 6 = 18; pair factors are(3, 6)
2 x 9 = 18; pair factors are(2, 9)
So (1, 18), (3, 6), and ( 2, 9), are the positive pair factors of 18
As we know that Factors of 18 include negative integers too.
List of all the negative pair factors of 18:
-1 x -18 = 18
-3 x -6 = 18
-2 x -9 = 18
So (-1, -18), (-3, -6) and ( -2, -9) are the negative pair factors of 18
Now we will study what is the prime factorization of 18.
What is the Prime Factorization of 18?
According to the prime factor definition, we know that the prime factor of a number is the product of all the factors that are prime, which is a number that divides by itself and only one. Hence we can list the prime factors from the list of factors of 18.
Or the other way to find the prime factorization of 18 is by prime factorization or by factor tree of 18.
Now let us study prime factors of 18 by division method.
Prime Factors of 18 by Division Method
To calculate the prime factors of 18 by the division method, first, take the least prime number that is 2. Divide it by 2 until it is completely divisible by 2. If at a point it is not divisible by 2 take the next least prime number that is 3. Perform the same steps and move forward, till we get 1, as the quotient. Here is the stepwise method to calculate the prime factors of 18
Step 1: Divide 18 with 2
18 ÷ 2 = 9
Step 2: Divide 9 with 2
9 ÷ 2 = not divisible
Step 3: So take another prime number 3 divide with 3
9 ÷ 3 = 3
Step 4: Now again divide 3 by 3
3 ÷ 3 = 1
We get the quotient 1.
From the above steps, we get a prime factor of 18 as 2 x 3 x 3 = 2 x 32
Here is the factor tree of 18.
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Solved Examples
Example 1: Find the Prime Factors of 180.
Solution:
180 = 2 x 90
= 2 x 2 x 45
= 2 x 2 x 5 x 9
= 2 x 2 x 5 x 3 x 3
This is all about the factors of 18 and how to calculate them. Learn how the factors of a number can be calculated step by step and utilize the process for determining the factors of other numbers on your own.
FAQs on Factors of 18
1. What do you mean by a Factor Tree?
A factor tree is an easy diagram to determine the factors of a number, usually a large number. It is like a tree with each branch of the tree being split into the factors of the number thus splitting a large number into its factors. The splitting of branches ends only when the factor at the end of the branch is a prime number which can only further be split into only two factors of 1 and the number itself.
The treetop is the number whose factors are to be found. The first branches of the tree will include one least prime number which can be a factor of the number and the rest composite number which can be further solicited to factors until finally only the prime numbers remain at the end of the tree branches and the splitting stops.
2. What are the Multiples of a Number?
Multiples are the number that divides the number completely without the remainder. Multiples are the product of a given number with an integer. For example, we can say that multiples of 8 are the numbers obtained by the product of 8 with the natural numbers like 1, 2, 3, 4,....so on. Some of the multiples of 8 are 8, 16, 24, 32, 40, 48, and so on….It is impossible to list all multiples of 8 since there are an infinite number of natural numbers.
3. How to find the factors of a given number?
It is quite easy to find the factors of a specific given number. We can do this by simply following the below steps:
Firstly, list all the numbers equal to or less than the given number
Then divide the given original number by each of these numbers which are less than or equal to the number.
Finally, all the numbers which have left no remainder when they divided the original number are considered as the factors of the given number.
4. What are the characteristics of a factor?
Some important characteristics of factor are listed below which will help one to find the factors of a given number:
The factor will divide the number whose factor it is evenly without leaving any reminder.
A common factor applicable for all numbers is one.
A number can be a factor of the parent number only if it is less than or equal to that number.
The number itself can be its greatest factor.
Only two factors are possible for a prime number: The number itself and one
More than two factors of a number mean it is a composite number.
Factors can never be a fraction
Factors are integers both positive and negative.
5. What is the relation between Factor and Multiple?
Factors and multiples are just the two sides of a coin. They go hand in hand along with each other. A multiple can be found by multiplying two factors. The product of two factors is multiple. Together they form the core of mathematics. They both use the operation of multiplication. Factors are the numbers that multiply to give the original number while multiple is the number that is obtained after multiplying a factor of that number by another factor thus forming the vice versa operation among them just like the opposite sides of a coin.
