GCF of 3 and 12
GCF of 3 and 12 is the largest possible number that divides 3 and 12 exactly without any remainder. The factors of 3 and 12 are 1, 3 and 1, 2, 3, 4, 6, 12 respectively. There are 3 commonly used methods to find the GCF of 3 and 12  long division, Euclidean algorithm, and prime factorization.
1.  GCF of 3 and 12 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 3 and 12?
Answer: GCF of 3 and 12 is 3.
Explanation:
The GCF of two nonzero integers, x(3) and y(12), is the greatest positive integer m(3) that divides both x(3) and y(12) without any remainder.
Methods to Find GCF of 3 and 12
The methods to find the GCF of 3 and 12 are explained below.
 Listing Common Factors
 Long Division Method
 Prime Factorization Method
GCF of 3 and 12 by Listing Common Factors
 Factors of 3: 1, 3
 Factors of 12: 1, 2, 3, 4, 6, 12
There are 2 common factors of 3 and 12, that are 1 and 3. Therefore, the greatest common factor of 3 and 12 is 3.
GCF of 3 and 12 by Long Division
GCF of 3 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 3 (smaller number).
 Step 2: Since the remainder = 0, the divisor (3) is the GCF of 3 and 12.
The corresponding divisor (3) is the GCF of 3 and 12.
GCF of 3 and 12 by Prime Factorization
Prime factorization of 3 and 12 is (3) and (2 × 2 × 3) respectively. As visible, 3 and 12 have only one common prime factor i.e. 3. Hence, the GCF of 3 and 12 is 3.
☛ Also Check:
 GCF of 90 and 135 = 45
 GCF of 24 and 42 = 6
 GCF of 36 and 81 = 9
 GCF of 51 and 68 = 17
 GCF of 4 and 16 = 4
 GCF of 30 and 54 = 6
 GCF of 25 and 60 = 5
GCF of 3 and 12 Examples

Example 1: Find the greatest number that divides 3 and 12 exactly.
Solution:
The greatest number that divides 3 and 12 exactly is their greatest common factor, i.e. GCF of 3 and 12.
⇒ Factors of 3 and 12: Factors of 3 = 1, 3
 Factors of 12 = 1, 2, 3, 4, 6, 12
Therefore, the GCF of 3 and 12 is 3.

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