GCF of 56 and 72
GCF of 56 and 72 is the largest possible number that divides 56 and 72 exactly without any remainder. The factors of 56 and 72 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the GCF of 56 and 72  prime factorization, long division, and Euclidean algorithm.
1.  GCF of 56 and 72 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 56 and 72?
Answer: GCF of 56 and 72 is 8.
Explanation:
The GCF of two nonzero integers, x(56) and y(72), is the greatest positive integer m(8) that divides both x(56) and y(72) without any remainder.
Methods to Find GCF of 56 and 72
Let's look at the different methods for finding the GCF of 56 and 72.
 Prime Factorization Method
 Using Euclid's Algorithm
 Listing Common Factors
GCF of 56 and 72 by Prime Factorization
Prime factorization of 56 and 72 is (2 × 2 × 2 × 7) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 56 and 72 have common prime factors. Hence, the GCF of 56 and 72 is 2 × 2 × 2 = 8.
GCF of 56 and 72 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 = 72 and Y = 56
 GCF(72, 56) = GCF(56, 72 mod 56) = GCF(56, 16)
 GCF(56, 16) = GCF(16, 56 mod 16) = GCF(16, 8)
 GCF(16, 8) = GCF(8, 16 mod 8) = GCF(8, 0)
 GCF(8, 0) = 8 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 56 and 72 is 8.
GCF of 56 and 72 by Listing Common Factors
 Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
There are 4 common factors of 56 and 72, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 56 and 72 is 8.
☛ Also Check:
 GCF of 12 and 72 = 12
 GCF of 15 and 40 = 5
 GCF of 56 and 98 = 14
 GCF of 27 and 72 = 9
 GCF of 84 and 96 = 12
 GCF of 7 and 35 = 7
 GCF of 34 and 85 = 17
GCF of 56 and 72 Examples

Example 1: Find the greatest number that divides 56 and 72 exactly.
Solution:
The greatest number that divides 56 and 72 exactly is their greatest common factor, i.e. GCF of 56 and 72.
⇒ Factors of 56 and 72: Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
 Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the GCF of 56 and 72 is 8.

Example 2: Find the GCF of 56 and 72, if their LCM is 504.
Solution:
∵ LCM × GCF = 56 × 72
⇒ GCF(56, 72) = (56 × 72)/504 = 8
Therefore, the greatest common factor of 56 and 72 is 8. 
Example 3: For two numbers, GCF = 8 and LCM = 504. If one number is 56, find the other number.
Solution:
Given: GCF (y, 56) = 8 and LCM (y, 56) = 504
∵ GCF × LCM = 56 × (y)
⇒ y = (GCF × LCM)/56
⇒ y = (8 × 504)/56
⇒ y = 72
Therefore, the other number is 72.
FAQs on GCF of 56 and 72
What is the GCF of 56 and 72?
The GCF of 56 and 72 is 8. To calculate the GCF (Greatest Common Factor) of 56 and 72, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 56 and 72, i.e., 8.
What is the Relation Between LCM and GCF of 56, 72?
The following equation can be used to express the relation between LCM and GCF of 56 and 72, i.e. GCF × LCM = 56 × 72.
How to Find the GCF of 56 and 72 by Long Division Method?
To find the GCF of 56, 72 using long division method, 72 is divided by 56. The corresponding divisor (8) when remainder equals 0 is taken as GCF.
If the GCF of 72 and 56 is 8, Find its LCM.
GCF(72, 56) × LCM(72, 56) = 72 × 56
Since the GCF of 72 and 56 = 8
⇒ 8 × LCM(72, 56) = 4032
Therefore, LCM = 504
☛ Greatest Common Factor Calculator
How to Find the GCF of 56 and 72 by Prime Factorization?
To find the GCF of 56 and 72, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 56 and 72. Hence, GCF(56, 72) = 2 × 2 × 2 = 8
☛ Prime Numbers
What are the Methods to Find GCF of 56 and 72?
There are three commonly used methods to find the GCF of 56 and 72.
 By Long Division
 By Listing Common Factors
 By Prime Factorization
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