GCF of 28 and 36
GCF of 28 and 36 is the largest possible number that divides 28 and 36 exactly without any remainder. The factors of 28 and 36 are 1, 2, 4, 7, 14, 28 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 28 and 36  prime factorization, Euclidean algorithm, and long division.
1.  GCF of 28 and 36 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 28 and 36?
Answer: GCF of 28 and 36 is 4.
Explanation:
The GCF of two nonzero integers, x(28) and y(36), is the greatest positive integer m(4) that divides both x(28) and y(36) without any remainder.
Methods to Find GCF of 28 and 36
The methods to find the GCF of 28 and 36 are explained below.
 Long Division Method
 Listing Common Factors
 Prime Factorization Method
GCF of 28 and 36 by Long Division
GCF of 28 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 36 (larger number) by 28 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (8).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (4) is the GCF of 28 and 36.
GCF of 28 and 36 by Listing Common Factors
 Factors of 28: 1, 2, 4, 7, 14, 28
 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
There are 3 common factors of 28 and 36, that are 1, 2, and 4. Therefore, the greatest common factor of 28 and 36 is 4.
GCF of 28 and 36 by Prime Factorization
Prime factorization of 28 and 36 is (2 × 2 × 7) and (2 × 2 × 3 × 3) respectively. As visible, 28 and 36 have common prime factors. Hence, the GCF of 28 and 36 is 2 × 2 = 4.
☛ Also Check:
 GCF of 20 and 30 = 10
 GCF of 64 and 80 = 16
 GCF of 3 and 9 = 3
 GCF of 42 and 63 = 21
 GCF of 24 and 54 = 6
 GCF of 60 and 75 = 15
 GCF of 36 and 63 = 9
GCF of 28 and 36 Examples

Example 1: Find the GCF of 28 and 36, if their LCM is 252.
Solution:
∵ LCM × GCF = 28 × 36
⇒ GCF(28, 36) = (28 × 36)/252 = 4
Therefore, the greatest common factor of 28 and 36 is 4. 
Example 2: Find the greatest number that divides 28 and 36 exactly.
Solution:
The greatest number that divides 28 and 36 exactly is their greatest common factor, i.e. GCF of 28 and 36.
⇒ Factors of 28 and 36: Factors of 28 = 1, 2, 4, 7, 14, 28
 Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the GCF of 28 and 36 is 4.

Example 3: The product of two numbers is 1008. If their GCF is 4, what is their LCM?
Solution:
Given: GCF = 4 and product of numbers = 1008
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1008/4
Therefore, the LCM is 252.
FAQs on GCF of 28 and 36
What is the GCF of 28 and 36?
The GCF of 28 and 36 is 4. To calculate the GCF of 28 and 36, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 28 and 36, i.e., 4.
How to Find the GCF of 28 and 36 by Long Division Method?
To find the GCF of 28, 36 using long division method, 36 is divided by 28. The corresponding divisor (4) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 28 and 36?
There are three commonly used methods to find the GCF of 28 and 36.
 By Euclidean Algorithm
 By Prime Factorization
 By Long Division
What is the Relation Between LCM and GCF of 28, 36?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 28 and 36, i.e. GCF × LCM = 28 × 36.
If the GCF of 36 and 28 is 4, Find its LCM.
GCF(36, 28) × LCM(36, 28) = 36 × 28
Since the GCF of 36 and 28 = 4
⇒ 4 × LCM(36, 28) = 1008
Therefore, LCM = 252
☛ Greatest Common Factor Calculator
How to Find the GCF of 28 and 36 by Prime Factorization?
To find the GCF of 28 and 36, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 28 and 36. Hence, GCF(28, 36) = 2 × 2 = 4
☛ What is a Prime Number?
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