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GCF of 42 and 56
GCF of 42 and 56 is the largest possible number that divides 42 and 56 exactly without any remainder. The factors of 42 and 56 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the GCF of 42 and 56 – prime factorization, Euclidean algorithm, and long division.
1.  GCF of 42 and 56 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 42 and 56?
Answer: GCF of 42 and 56 is 14.
Explanation:
The GCF of two nonzero integers, x(42) and y(56), is the greatest positive integer m(14) that divides both x(42) and y(56) without any remainder.
Methods to Find GCF of 42 and 56
The methods to find the GCF of 42 and 56 are explained below.
 Listing Common Factors
 Long Division Method
 Prime Factorization Method
GCF of 42 and 56 by Listing Common Factors
 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
 Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
There are 4 common factors of 42 and 56, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 42 and 56 is 14.
GCF of 42 and 56 by Long Division
GCF of 42 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 42 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (14).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (14) is the GCF of 42 and 56.
GCF of 42 and 56 by Prime Factorization
Prime factorization of 42 and 56 is (2 × 3 × 7) and (2 × 2 × 2 × 7) respectively. As visible, 42 and 56 have common prime factors. Hence, the GCF of 42 and 56 is 2 × 7 = 14.
☛ Also Check:
 GCF of 20 and 100 = 20
 GCF of 32 and 56 = 8
 GCF of 64 and 72 = 8
 GCF of 96 and 144 = 48
 GCF of 3 and 15 = 3
 GCF of 32 and 81 = 1
 GCF of 70 and 21 = 7
GCF of 42 and 56 Examples

Example 1: Find the GCF of 42 and 56, if their LCM is 168.
Solution:
∵ LCM × GCF = 42 × 56
⇒ GCF(42, 56) = (42 × 56)/168 = 14
Therefore, the greatest common factor of 42 and 56 is 14. 
Example 2: The product of two numbers is 2352. If their GCF is 14, what is their LCM?
Solution:
Given: GCF = 14 and product of numbers = 2352
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2352/14
Therefore, the LCM is 168. 
Example 3: Find the greatest number that divides 42 and 56 exactly.
Solution:
The greatest number that divides 42 and 56 exactly is their greatest common factor, i.e. GCF of 42 and 56.
⇒ Factors of 42 and 56:
 Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
 Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Therefore, the GCF of 42 and 56 is 14.
FAQs on GCF of 42 and 56
What is the GCF of 42 and 56?
The GCF of 42 and 56 is 14. To calculate the GCF of 42 and 56, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and choose the greatest factor that exactly divides both 42 and 56, i.e., 14.
What is the Relation Between LCM and GCF of 42, 56?
The following equation can be used to express the relation between Least Common Multiple and GCF of 42 and 56, i.e. GCF × LCM = 42 × 56.
What are the Methods to Find GCF of 42 and 56?
There are three commonly used methods to find the GCF of 42 and 56.
 By Prime Factorization
 By Euclidean Algorithm
 By Long Division
How to Find the GCF of 42 and 56 by Long Division Method?
To find the GCF of 42, 56 using long division method, 56 is divided by 42. The corresponding divisor (14) when remainder equals 0 is taken as GCF.
If the GCF of 56 and 42 is 14, Find its LCM.
GCF(56, 42) × LCM(56, 42) = 56 × 42
Since the GCF of 56 and 42 = 14
⇒ 14 × LCM(56, 42) = 2352
Therefore, LCM = 168
☛ Greatest Common Factor Calculator
How to Find the GCF of 42 and 56 by Prime Factorization?
To find the GCF of 42 and 56, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 56 = 2 × 2 × 2 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 42 and 56. Hence, GCF(42, 56) = 2 × 7 = 14
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