GCF of 18 and 81
GCF of 18 and 81 is the largest possible number that divides 18 and 81 exactly without any remainder. The factors of 18 and 81 are 1, 2, 3, 6, 9, 18 and 1, 3, 9, 27, 81 respectively. There are 3 commonly used methods to find the GCF of 18 and 81  long division, Euclidean algorithm, and prime factorization.
1.  GCF of 18 and 81 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 18 and 81?
Answer: GCF of 18 and 81 is 9.
Explanation:
The GCF of two nonzero integers, x(18) and y(81), is the greatest positive integer m(9) that divides both x(18) and y(81) without any remainder.
Methods to Find GCF of 18 and 81
Let's look at the different methods for finding the GCF of 18 and 81.
 Listing Common Factors
 Long Division Method
 Prime Factorization Method
GCF of 18 and 81 by Listing Common Factors
 Factors of 18: 1, 2, 3, 6, 9, 18
 Factors of 81: 1, 3, 9, 27, 81
There are 3 common factors of 18 and 81, that are 1, 3, and 9. Therefore, the greatest common factor of 18 and 81 is 9.
GCF of 18 and 81 by Long Division
GCF of 18 and 81 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 81 (larger number) by 18 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (9).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (9) is the GCF of 18 and 81.
GCF of 18 and 81 by Prime Factorization
Prime factorization of 18 and 81 is (2 × 3 × 3) and (3 × 3 × 3 × 3) respectively. As visible, 18 and 81 have common prime factors. Hence, the GCF of 18 and 81 is 3 × 3 = 9.
☛ Also Check:
 GCF of 17 and 51 = 17
 GCF of 7 and 35 = 7
 GCF of 75 and 100 = 25
 GCF of 75 and 125 = 25
 GCF of 48 and 56 = 8
 GCF of 42, 28 and 70 = 14
 GCF of 15 and 18 = 3
GCF of 18 and 81 Examples

Example 1: For two numbers, GCF = 9 and LCM = 162. If one number is 81, find the other number.
Solution:
Given: GCF (y, 81) = 9 and LCM (y, 81) = 162
∵ GCF × LCM = 81 × (y)
⇒ y = (GCF × LCM)/81
⇒ y = (9 × 162)/81
⇒ y = 18
Therefore, the other number is 18. 
Example 2: Find the GCF of 18 and 81, if their LCM is 162.
Solution:
∵ LCM × GCF = 18 × 81
⇒ GCF(18, 81) = (18 × 81)/162 = 9
Therefore, the greatest common factor of 18 and 81 is 9. 
Example 3: The product of two numbers is 1458. If their GCF is 9, what is their LCM?
Solution:
Given: GCF = 9 and product of numbers = 1458
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1458/9
Therefore, the LCM is 162.
FAQs on GCF of 18 and 81
What is the GCF of 18 and 81?
The GCF of 18 and 81 is 9. To calculate the GCF (Greatest Common Factor) of 18 and 81, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 81 = 1, 3, 9, 27, 81) and choose the greatest factor that exactly divides both 18 and 81, i.e., 9.
How to Find the GCF of 18 and 81 by Long Division Method?
To find the GCF of 18, 81 using long division method, 81 is divided by 18. The corresponding divisor (9) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 18, 81?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 18 and 81, i.e. GCF × LCM = 18 × 81.
How to Find the GCF of 18 and 81 by Prime Factorization?
To find the GCF of 18 and 81, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 81 = 3 × 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 18 and 81. Hence, GCF(18, 81) = 3 × 3 = 9
☛ Prime Numbers
What are the Methods to Find GCF of 18 and 81?
There are three commonly used methods to find the GCF of 18 and 81.
 By Prime Factorization
 By Long Division
 By Euclidean Algorithm
If the GCF of 81 and 18 is 9, Find its LCM.
GCF(81, 18) × LCM(81, 18) = 81 × 18
Since the GCF of 81 and 18 = 9
⇒ 9 × LCM(81, 18) = 1458
Therefore, LCM = 162
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