GCF of 84 and 42
GCF of 84 and 42 is the largest possible number that divides 84 and 42 exactly without any remainder. The factors of 84 and 42 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 84 and 42  long division, Euclidean algorithm, and prime factorization.
1.  GCF of 84 and 42 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 84 and 42?
Answer: GCF of 84 and 42 is 42.
Explanation:
The GCF of two nonzero integers, x(84) and y(42), is the greatest positive integer m(42) that divides both x(84) and y(42) without any remainder.
Methods to Find GCF of 84 and 42
The methods to find the GCF of 84 and 42 are explained below.
 Long Division Method
 Using Euclid's Algorithm
 Listing Common Factors
GCF of 84 and 42 by Long Division
GCF of 84 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 84 (larger number) by 42 (smaller number).
 Step 2: Since the remainder = 0, the divisor (42) is the GCF of 84 and 42.
The corresponding divisor (42) is the GCF of 84 and 42.
GCF of 84 and 42 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 = 84 and Y = 42
 GCF(84, 42) = GCF(42, 84 mod 42) = GCF(42, 0)
 GCF(42, 0) = 42 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 84 and 42 is 42.
GCF of 84 and 42 by Listing Common Factors
 Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 8 common factors of 84 and 42, that are 1, 2, 3, 6, 7, 42, 14, and 21. Therefore, the greatest common factor of 84 and 42 is 42.
☛ Also Check:
 GCF of 24 and 54 = 6
 GCF of 16 and 64 = 16
 GCF of 20 and 70 = 10
 GCF of 12 and 72 = 12
 GCF of 86 and 42 = 2
 GCF of 12 and 24 = 12
 GCF of 6 and 12 = 6
GCF of 84 and 42 Examples

Example 1: Find the greatest number that divides 84 and 42 exactly.
Solution:
The greatest number that divides 84 and 42 exactly is their greatest common factor, i.e. GCF of 84 and 42.
⇒ Factors of 84 and 42: Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
 Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
Therefore, the GCF of 84 and 42 is 42.

Example 2: The product of two numbers is 3528. If their GCF is 42, what is their LCM?
Solution:
Given: GCF = 42 and product of numbers = 3528
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3528/42
Therefore, the LCM is 84. 
Example 3: Find the GCF of 84 and 42, if their LCM is 84.
Solution:
∵ LCM × GCF = 84 × 42
⇒ GCF(84, 42) = (84 × 42)/84 = 42
Therefore, the greatest common factor of 84 and 42 is 42.
FAQs on GCF of 84 and 42
What is the GCF of 84 and 42?
The GCF of 84 and 42 is 42. To calculate the greatest common factor of 84 and 42, we need to factor each number (factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 84 and 42, i.e., 42.
What is the Relation Between LCM and GCF of 84, 42?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 84 and 42, i.e. GCF × LCM = 84 × 42.
What are the Methods to Find GCF of 84 and 42?
There are three commonly used methods to find the GCF of 84 and 42.
 By Prime Factorization
 By Euclidean Algorithm
 By Long Division
How to Find the GCF of 84 and 42 by Long Division Method?
To find the GCF of 84, 42 using long division method, 84 is divided by 42. The corresponding divisor (42) when remainder equals 0 is taken as GCF.
How to Find the GCF of 84 and 42 by Prime Factorization?
To find the GCF of 84 and 42, we will find the prime factorization of the given numbers, i.e. 84 = 2 × 2 × 3 × 7; 42 = 2 × 3 × 7.
⇒ Since 2, 3, 7 are common terms in the prime factorization of 84 and 42. Hence, GCF(84, 42) = 2 × 3 × 7 = 42
☛ What are Prime Numbers?
If the GCF of 42 and 84 is 42, Find its LCM.
GCF(42, 84) × LCM(42, 84) = 42 × 84
Since the GCF of 42 and 84 = 42
⇒ 42 × LCM(42, 84) = 3528
Therefore, LCM = 84
☛ GCF Calculator
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