GCF of 12 and 56
GCF of 12 and 56 is the largest possible number that divides 12 and 56 exactly without any remainder. The factors of 12 and 56 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the GCF of 12 and 56  Euclidean algorithm, prime factorization, and long division.
1.  GCF of 12 and 56 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 12 and 56?
Answer: GCF of 12 and 56 is 4.
Explanation:
The GCF of two nonzero integers, x(12) and y(56), is the greatest positive integer m(4) that divides both x(12) and y(56) without any remainder.
Methods to Find GCF of 12 and 56
Let's look at the different methods for finding the GCF of 12 and 56.
 Listing Common Factors
 Using Euclid's Algorithm
 Long Division Method
GCF of 12 and 56 by Listing Common Factors
 Factors of 12: 1, 2, 3, 4, 6, 12
 Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
There are 3 common factors of 12 and 56, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 56 is 4.
GCF of 12 and 56 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 = 56 and Y = 12
 GCF(56, 12) = GCF(12, 56 mod 12) = GCF(12, 8)
 GCF(12, 8) = GCF(8, 12 mod 8) = GCF(8, 4)
 GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
 GCF(4, 0) = 4 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 12 and 56 is 4.
GCF of 12 and 56 by Long Division
GCF of 12 and 56 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 56 (larger number) by 12 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (8).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (4) is the GCF of 12 and 56.
☛ Also Check:
 GCF of 7 and 8 = 1
 GCF of 77 and 56 = 7
 GCF of 14 and 42 = 14
 GCF of 36 and 100 = 4
 GCF of 56 and 98 = 14
 GCF of 5 and 7 = 1
 GCF of 48 and 56 = 8
GCF of 12 and 56 Examples

Example 1: Find the GCF of 12 and 56, if their LCM is 168.
Solution:
∵ LCM × GCF = 12 × 56
⇒ GCF(12, 56) = (12 × 56)/168 = 4
Therefore, the greatest common factor of 12 and 56 is 4. 
Example 2: For two numbers, GCF = 4 and LCM = 168. If one number is 56, find the other number.
Solution:
Given: GCF (y, 56) = 4 and LCM (y, 56) = 168
∵ GCF × LCM = 56 × (y)
⇒ y = (GCF × LCM)/56
⇒ y = (4 × 168)/56
⇒ y = 12
Therefore, the other number is 12. 
Example 3: Find the greatest number that divides 12 and 56 exactly.
Solution:
The greatest number that divides 12 and 56 exactly is their greatest common factor, i.e. GCF of 12 and 56.
⇒ Factors of 12 and 56: Factors of 12 = 1, 2, 3, 4, 6, 12
 Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Therefore, the GCF of 12 and 56 is 4.
FAQs on GCF of 12 and 56
What is the GCF of 12 and 56?
The GCF of 12 and 56 is 4. To calculate the GCF (Greatest Common Factor) of 12 and 56, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and choose the greatest factor that exactly divides both 12 and 56, i.e., 4.
How to Find the GCF of 12 and 56 by Prime Factorization?
To find the GCF of 12 and 56, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 56 = 2 × 2 × 2 × 7.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 56. Hence, GCF(12, 56) = 2 × 2 = 4
☛ What are Prime Numbers?
If the GCF of 56 and 12 is 4, Find its LCM.
GCF(56, 12) × LCM(56, 12) = 56 × 12
Since the GCF of 56 and 12 = 4
⇒ 4 × LCM(56, 12) = 672
Therefore, LCM = 168
☛ GCF Calculator
What are the Methods to Find GCF of 12 and 56?
There are three commonly used methods to find the GCF of 12 and 56.
 By Listing Common Factors
 By Long Division
 By Prime Factorization
How to Find the GCF of 12 and 56 by Long Division Method?
To find the GCF of 12, 56 using long division method, 56 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 12, 56?
The following equation can be used to express the relation between LCM and GCF of 12 and 56, i.e. GCF × LCM = 12 × 56.
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