GCF of 36 and 99
GCF of 36 and 99 is the largest possible number that divides 36 and 99 exactly without any remainder. The factors of 36 and 99 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 3, 9, 11, 33, 99 respectively. There are 3 commonly used methods to find the GCF of 36 and 99  prime factorization, long division, and Euclidean algorithm.
1.  GCF of 36 and 99 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 36 and 99?
Answer: GCF of 36 and 99 is 9.
Explanation:
The GCF of two nonzero integers, x(36) and y(99), is the greatest positive integer m(9) that divides both x(36) and y(99) without any remainder.
Methods to Find GCF of 36 and 99
Let's look at the different methods for finding the GCF of 36 and 99.
 Listing Common Factors
 Prime Factorization Method
 Using Euclid's Algorithm
GCF of 36 and 99 by Listing Common Factors
 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 99: 1, 3, 9, 11, 33, 99
There are 3 common factors of 36 and 99, that are 1, 3, and 9. Therefore, the greatest common factor of 36 and 99 is 9.
GCF of 36 and 99 by Prime Factorization
Prime factorization of 36 and 99 is (2 × 2 × 3 × 3) and (3 × 3 × 11) respectively. As visible, 36 and 99 have common prime factors. Hence, the GCF of 36 and 99 is 3 × 3 = 9.
GCF of 36 and 99 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 99 and Y = 36
 GCF(99, 36) = GCF(36, 99 mod 36) = GCF(36, 27)
 GCF(36, 27) = GCF(27, 36 mod 27) = GCF(27, 9)
 GCF(27, 9) = GCF(9, 27 mod 9) = GCF(9, 0)
 GCF(9, 0) = 9 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 36 and 99 is 9.
☛ Also Check:
 GCF of 12 and 42 = 6
 GCF of 13 and 26 = 13
 GCF of 55 and 75 = 5
 GCF of 24 and 42 = 6
 GCF of 54 and 27 = 27
 GCF of 24 and 60 = 12
 GCF of 35 and 50 = 5
GCF of 36 and 99 Examples

Example 1: The product of two numbers is 3564. If their GCF is 9, what is their LCM?
Solution:
Given: GCF = 9 and product of numbers = 3564
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3564/9
Therefore, the LCM is 396. 
Example 2: Find the GCF of 36 and 99, if their LCM is 396.
Solution:
∵ LCM × GCF = 36 × 99
⇒ GCF(36, 99) = (36 × 99)/396 = 9
Therefore, the greatest common factor of 36 and 99 is 9. 
Example 3: For two numbers, GCF = 9 and LCM = 396. If one number is 99, find the other number.
Solution:
Given: GCF (y, 99) = 9 and LCM (y, 99) = 396
∵ GCF × LCM = 99 × (y)
⇒ y = (GCF × LCM)/99
⇒ y = (9 × 396)/99
⇒ y = 36
Therefore, the other number is 36.
FAQs on GCF of 36 and 99
What is the GCF of 36 and 99?
The GCF of 36 and 99 is 9. To calculate the GCF (Greatest Common Factor) of 36 and 99, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 99 = 1, 3, 9, 11, 33, 99) and choose the greatest factor that exactly divides both 36 and 99, i.e., 9.
What are the Methods to Find GCF of 36 and 99?
There are three commonly used methods to find the GCF of 36 and 99.
 By Prime Factorization
 By Listing Common Factors
 By Long Division
If the GCF of 99 and 36 is 9, Find its LCM.
GCF(99, 36) × LCM(99, 36) = 99 × 36
Since the GCF of 99 and 36 = 9
⇒ 9 × LCM(99, 36) = 3564
Therefore, LCM = 396
☛ GCF Calculator
What is the Relation Between LCM and GCF of 36, 99?
The following equation can be used to express the relation between LCM and GCF of 36 and 99, i.e. GCF × LCM = 36 × 99.
How to Find the GCF of 36 and 99 by Long Division Method?
To find the GCF of 36, 99 using long division method, 99 is divided by 36. The corresponding divisor (9) when remainder equals 0 is taken as GCF.
How to Find the GCF of 36 and 99 by Prime Factorization?
To find the GCF of 36 and 99, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 99 = 3 × 3 × 11.
⇒ Since 3, 3 are common terms in the prime factorization of 36 and 99. Hence, GCF(36, 99) = 3 × 3 = 9
☛ What are Prime Numbers?
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