GCF of 8 and 12
GCF of 8 and 12 is the largest possible number that divides 8 and 12 exactly without any remainder. The factors of 8 and 12 are 1, 2, 4, 8 and 1, 2, 3, 4, 6, 12 respectively. There are 3 commonly used methods to find the GCF of 8 and 12  long division, prime factorization, and Euclidean algorithm.
1.  GCF of 8 and 12 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 8 and 12?
Answer: GCF of 8 and 12 is 4.
Explanation:
The GCF of two nonzero integers, x(8) and y(12), is the greatest positive integer m(4) that divides both x(8) and y(12) without any remainder.
Methods to Find GCF of 8 and 12
The methods to find the GCF of 8 and 12 are explained below.
 Listing Common Factors
 Prime Factorization Method
 Long Division Method
GCF of 8 and 12 by Listing Common Factors
 Factors of 8: 1, 2, 4, 8
 Factors of 12: 1, 2, 3, 4, 6, 12
There are 3 common factors of 8 and 12, that are 1, 2, and 4. Therefore, the greatest common factor of 8 and 12 is 4.
GCF of 8 and 12 by Prime Factorization
Prime factorization of 8 and 12 is (2 × 2 × 2) and (2 × 2 × 3) respectively. As visible, 8 and 12 have common prime factors. Hence, the GCF of 8 and 12 is 2 × 2 = 4.
GCF of 8 and 12 by Long Division
GCF of 8 and 12 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 12 (larger number) by 8 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (4).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (4) is the GCF of 8 and 12.
☛ Also Check:
 GCF of 32 and 72 = 8
 GCF of 16 and 72 = 8
 GCF of 45 and 60 = 15
 GCF of 18 and 32 = 2
 GCF of 21 and 49 = 7
 GCF of 16 and 48 = 16
 GCF of 20 and 36 = 4
GCF of 8 and 12 Examples

Example 1: The product of two numbers is 96. If their GCF is 4, what is their LCM?
Solution:
Given: GCF = 4 and product of numbers = 96
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 96/4
Therefore, the LCM is 24. 
Example 2: Find the GCF of 8 and 12, if their LCM is 24.
Solution:
∵ LCM × GCF = 8 × 12
⇒ GCF(8, 12) = (8 × 12)/24 = 4
Therefore, the greatest common factor of 8 and 12 is 4. 
Example 3: For two numbers, GCF = 4 and LCM = 24. If one number is 8, find the other number.
Solution:
Given: GCF (y, 8) = 4 and LCM (y, 8) = 24
∵ GCF × LCM = 8 × (y)
⇒ y = (GCF × LCM)/8
⇒ y = (4 × 24)/8
⇒ y = 12
Therefore, the other number is 12.
FAQs on GCF of 8 and 12
What is the GCF of 8 and 12?
The GCF of 8 and 12 is 4. To calculate the GCF of 8 and 12, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest factor that exactly divides both 8 and 12, i.e., 4.
What is the Relation Between LCM and GCF of 8, 12?
The following equation can be used to express the relation between LCM and GCF of 8 and 12, i.e. GCF × LCM = 8 × 12.
How to Find the GCF of 8 and 12 by Long Division Method?
To find the GCF of 8, 12 using long division method, 12 is divided by 8. The corresponding divisor (4) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 8 and 12?
There are three commonly used methods to find the GCF of 8 and 12.
 By Long Division
 By Prime Factorization
 By Euclidean Algorithm
If the GCF of 12 and 8 is 4, Find its LCM.
GCF(12, 8) × LCM(12, 8) = 12 × 8
Since the GCF of 12 and 8 = 4
⇒ 4 × LCM(12, 8) = 96
Therefore, LCM = 24
☛ GCF Calculator
How to Find the GCF of 8 and 12 by Prime Factorization?
To find the GCF of 8 and 12, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 12 = 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 8 and 12. Hence, GCF(8, 12) = 2 × 2 = 4
☛ What is a Prime Number?
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