Factors of 18 are 1, 2, 3, 6, 9 and 18. The factors are the number that divides the original number completely without leaving any remainder and the factors pairs of a number are the ones that give back the original number when multiplied in pairs. The number 18 has 4 factors other than 1 and itself and it is a composite number because it has more factors other than 1 and the number itself.
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In this article, we are going to learn what are the factors of 18, prime factors of 18 and how to find factors along with some examples based on this concept.
Table of Content
What is a Factor?
Factors are the building blocks of a number, these are the integers that divide the original number without leaving any remainder. Every positive integer has at least two factors: 1 and the number itself. Numbers are further classified as prime numbers or composite numbers based on their factors.
For example:
- Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- Factors of 12 are 1, 2, 3, 4, 6, and 12.
Read More, Factors of a number.
What are the Factors of 18?
Factors of 18 are those number which gives the number 18 after multiplying with their pair. So, for the number 18 : 1, 2, 3, 6, 9 and 18 are the factors. These numbers are exactly divisible by 18. In simple words, 18 will always give a remainder as Zero (0) on dividing by these numbers
Factor of 18 | Division | Remainder |
|---|---|---|
1 | 18 ÷ 1 | 0 |
2 | 18 ÷ 2 | 0 |
3 | 18 ÷ 3 | 0 |
6 | 18 ÷ 6 | 0 |
9 | 18 ÷ 9 | 0 |
18 | 18 ÷ 18 | 0 |
In the above table, we can see that all the factors of 18 are completely divisible by 18, leaving remainder 0.
All Factors of 18
Here is a list of all the factors of 18:
Factors of 18 are 1, 2, 3, 6, 9 and 18.
Prime Factors of 18
Prime factors are those factors of a number which are prime and completly divisible by the original number. Prime factors when multiplied together gives back the original number.
The Prime factors of the number 18 are:
- 2 (As 2 is a prime number and completely divisible by 18)
- 3 (As 3 is a prime number and completely divisible by 18)
When we conclude the product of the Prime factors , we write 18 as 2 × 32 . This is because 18 can be divided into 2 × 3 × 3 , where 2 appears once and 3 appears twice .
How to Find Factors of 18?
To find all the factors of 18 , we can use the multiplication method. According to which we will find all the pairs of number which when multiplies together gives 18 as a result.
Steps for Multiplication method are:
- Start with 1 : Multiply 1 by 18, the result will be 18. (1 , 18) is the first factor pair for 18.
- Try with 2 : Multiply 2 by 9, the result will be 18. (2 , 9) is the other factor pair for 18.
- Try with 3 : Multiply 3 by 6, the result will be 18. (3 , 6) is the other factor pair for 18.
- Continue till we get all the required pairs.
Factors of 18 are:
- 1 × 18 = 18
- 2 × 9 = 18
- 3 × 6 = 18
So, the Factors of 18 are 1, 2, 3, 6, 9 and 18.
Prime Factorization of 18
Prime Factorization is a method of finding the prime factors by dividing the given number from a prime number. This factorization start from the smallest divisible prime number, and continue further till we get 1 as our quotient.
Therefore, we simply divide the given number to see which prime numbers it can be divided by. This method helps us identify all the prime factors of a number.
The process of division is explained below -:
Step 1: Start with 18.
Step 2: Divide by 2: 18 ÷ 2 = 9.
Step 3: Divide by 3: 9 ÷ 3 = 3.
Step 4: Divide by 3 : 3 ÷ 3 = 1
Read More, Prime Factorization.
Factor Tree of 18
A factor tree is a diagram that breaks down a number to their prime factors. In the factor tree method, we continue the division process until prime numbers appear at all the leaf nodes. Those prime numbers are the prime factor of the number.
Here’s a factor tree for the number 18:
Factor Pairs of 18
Factor Pairs of 18 are pairs of numbers that gives 18 by multiplying two factors such as (1 , 18). We consider all integers when forming factor pairs, including two negative numbers. If, upon multiplying these numbers, we obtain 18, it is also included in the factor pairs. Factor pairs can be positive as well as negative.
Positive Factor Pairs of 18
All the Positive factor pair of 18 are illustrated below:
Positive Factor Pair of 18 | Multiplication of Factor Pair of 18 |
|---|---|
(1 , 18) | 1 × 18 = 18 |
(2 , 9) | 2 × 9 = 18 |
(3 , 6) | 3 × 6 = 18 |
Negative Factor Pairs of 18
Below are all the Negative Factor Pairs of 18:
Negative Factor Pair of 18 | Multiplication of Factor Pair of 18 |
|---|---|
(-1 , -18) | -1 × -18 = 18 |
(-2 , -9) | -2 × -9 = 18 |
(-3 , -6) | -3 × -6 = 18 |
Read More,
Solved Examples on Factors of 18
Example 1: What is the sum of all the factors of 18?
Solution:
The factors of 18 are 1, 2, 3, 6, 9, and 18.Sum of the factors of 18 = 1 + 2 + 3 + 6 + 9 + 18Sum of the factors of 18 = 39
Example 2: What are the common factors of 18 and 6.
Solution:
The factors of 18 are {1, 2, 3, 6, 9, 18}.
The factors of 6 are {1, 3, 6}.
Hence, the common factors of 18 and 9 are {1, 3, 6}.
Example 3: What are the common factors of 7 and 18.
Solution:
Factors of 18 = 1, 2, 3, 6, 9 and 18.
Factors of 7 = 1 and 7.
The common factor of 7 and 18 is 1 only.
Example 4: What are the prime factorization of 18?
Solution:
The prime factorization of 18 is 2 × 3 × 3 or 2 × 32.
Example 5: What are the negative pair factors of 18?
Solution:
The negative pair factors of 18 are {-1, -18}, {-2, -9} and {-3, -6}.
Practice Questions on Factors of 18
Q1: What are the Product of all the prime factor of 18?
Q2: What are the common factor of 18 and 20 ?
Q3: What is the Smallest Prime factor of 18 ?
Q4: Find all the positive pairs of 18?
Q5: What are the common factors of any prime number and 18?