[Maths Class Notes] on Factors of 18 Pdf for Exam

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.