GCF of 18 and 66
GCF of 18 and 66 is the largest possible number that divides 18 and 66 exactly without any remainder. The factors of 18 and 66 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 6, 11, 22, 33, 66 respectively. There are 3 commonly used methods to find the GCF of 18 and 66  Euclidean algorithm, long division, and prime factorization.
1.  GCF of 18 and 66 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 18 and 66?
Answer: GCF of 18 and 66 is 6.
Explanation:
The GCF of two nonzero integers, x(18) and y(66), is the greatest positive integer m(6) that divides both x(18) and y(66) without any remainder.
Methods to Find GCF of 18 and 66
Let's look at the different methods for finding the GCF of 18 and 66.
 Listing Common Factors
 Prime Factorization Method
 Long Division Method
GCF of 18 and 66 by Listing Common Factors
 Factors of 18: 1, 2, 3, 6, 9, 18
 Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
There are 4 common factors of 18 and 66, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 18 and 66 is 6.
GCF of 18 and 66 by Prime Factorization
Prime factorization of 18 and 66 is (2 × 3 × 3) and (2 × 3 × 11) respectively. As visible, 18 and 66 have common prime factors. Hence, the GCF of 18 and 66 is 2 × 3 = 6.
GCF of 18 and 66 by Long Division
GCF of 18 and 66 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 66 (larger number) by 18 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (12).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 18 and 66.
☛ Also Check:
 GCF of 10 and 20 = 10
 GCF of 60 and 20 = 20
 GCF of 36 and 90 = 18
 GCF of 25 and 30 = 5
 GCF of 12 and 42 = 6
 GCF of 75 and 100 = 25
 GCF of 5 and 8 = 1
GCF of 18 and 66 Examples

Example 1: Find the GCF of 18 and 66, if their LCM is 198.
Solution:
∵ LCM × GCF = 18 × 66
⇒ GCF(18, 66) = (18 × 66)/198 = 6
Therefore, the greatest common factor of 18 and 66 is 6. 
Example 2: The product of two numbers is 1188. If their GCF is 6, what is their LCM?
Solution:
Given: GCF = 6 and product of numbers = 1188
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1188/6
Therefore, the LCM is 198. 
Example 3: For two numbers, GCF = 6 and LCM = 198. If one number is 18, find the other number.
Solution:
Given: GCF (x, 18) = 6 and LCM (x, 18) = 198
∵ GCF × LCM = 18 × (x)
⇒ x = (GCF × LCM)/18
⇒ x = (6 × 198)/18
⇒ x = 66
Therefore, the other number is 66.
FAQs on GCF of 18 and 66
What is the GCF of 18 and 66?
The GCF of 18 and 66 is 6. To calculate the greatest common factor of 18 and 66, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66) and choose the greatest factor that exactly divides both 18 and 66, i.e., 6.
How to Find the GCF of 18 and 66 by Prime Factorization?
To find the GCF of 18 and 66, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 66 = 2 × 3 × 11.
⇒ Since 2, 3 are common terms in the prime factorization of 18 and 66. Hence, GCF(18, 66) = 2 × 3 = 6
☛ Prime Numbers
How to Find the GCF of 18 and 66 by Long Division Method?
To find the GCF of 18, 66 using long division method, 66 is divided by 18. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
If the GCF of 66 and 18 is 6, Find its LCM.
GCF(66, 18) × LCM(66, 18) = 66 × 18
Since the GCF of 66 and 18 = 6
⇒ 6 × LCM(66, 18) = 1188
Therefore, LCM = 198
☛ Greatest Common Factor Calculator
What are the Methods to Find GCF of 18 and 66?
There are three commonly used methods to find the GCF of 18 and 66.
 By Prime Factorization
 By Long Division
 By Euclidean Algorithm
What is the Relation Between LCM and GCF of 18, 66?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 18 and 66, i.e. GCF × LCM = 18 × 66.
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