GCF of 63 and 84
GCF of 63 and 84 is the largest possible number that divides 63 and 84 exactly without any remainder. The factors of 63 and 84 are 1, 3, 7, 9, 21, 63 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 respectively. There are 3 commonly used methods to find the GCF of 63 and 84  prime factorization, long division, and Euclidean algorithm.
1.  GCF of 63 and 84 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 63 and 84?
Answer: GCF of 63 and 84 is 21.
Explanation:
The GCF of two nonzero integers, x(63) and y(84), is the greatest positive integer m(21) that divides both x(63) and y(84) without any remainder.
Methods to Find GCF of 63 and 84
The methods to find the GCF of 63 and 84 are explained below.
 Prime Factorization Method
 Using Euclid's Algorithm
 Long Division Method
GCF of 63 and 84 by Prime Factorization
Prime factorization of 63 and 84 is (3 × 3 × 7) and (2 × 2 × 3 × 7) respectively. As visible, 63 and 84 have common prime factors. Hence, the GCF of 63 and 84 is 3 × 7 = 21.
GCF of 63 and 84 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 = 63
 GCF(84, 63) = GCF(63, 84 mod 63) = GCF(63, 21)
 GCF(63, 21) = GCF(21, 63 mod 21) = GCF(21, 0)
 GCF(21, 0) = 21 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 63 and 84 is 21.
GCF of 63 and 84 by Long Division
GCF of 63 and 84 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 84 (larger number) by 63 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (63) by the remainder (21).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (21) is the GCF of 63 and 84.
☛ Also Check:
 GCF of 56 and 64 = 8
 GCF of 32 and 36 = 4
 GCF of 68 and 102 = 34
 GCF of 40 and 56 = 8
 GCF of 18 and 45 = 9
 GCF of 175 and 25 = 25
 GCF of 45 and 90 = 45
GCF of 63 and 84 Examples

Example 1: The product of two numbers is 5292. If their GCF is 21, what is their LCM?
Solution:
Given: GCF = 21 and product of numbers = 5292
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 5292/21
Therefore, the LCM is 252. 
Example 2: For two numbers, GCF = 21 and LCM = 252. If one number is 84, find the other number.
Solution:
Given: GCF (z, 84) = 21 and LCM (z, 84) = 252
∵ GCF × LCM = 84 × (z)
⇒ z = (GCF × LCM)/84
⇒ z = (21 × 252)/84
⇒ z = 63
Therefore, the other number is 63. 
Example 3: Find the greatest number that divides 63 and 84 exactly.
Solution:
The greatest number that divides 63 and 84 exactly is their greatest common factor, i.e. GCF of 63 and 84.
⇒ Factors of 63 and 84: Factors of 63 = 1, 3, 7, 9, 21, 63
 Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Therefore, the GCF of 63 and 84 is 21.
FAQs on GCF of 63 and 84
What is the GCF of 63 and 84?
The GCF of 63 and 84 is 21. To calculate the GCF of 63 and 84, we need to factor each number (factors of 63 = 1, 3, 7, 9, 21, 63; factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84) and choose the greatest factor that exactly divides both 63 and 84, i.e., 21.
How to Find the GCF of 63 and 84 by Long Division Method?
To find the GCF of 63, 84 using long division method, 84 is divided by 63. The corresponding divisor (21) when remainder equals 0 is taken as GCF.
How to Find the GCF of 63 and 84 by Prime Factorization?
To find the GCF of 63 and 84, we will find the prime factorization of the given numbers, i.e. 63 = 3 × 3 × 7; 84 = 2 × 2 × 3 × 7.
⇒ Since 3, 7 are common terms in the prime factorization of 63 and 84. Hence, GCF(63, 84) = 3 × 7 = 21
☛ Prime Numbers
If the GCF of 84 and 63 is 21, Find its LCM.
GCF(84, 63) × LCM(84, 63) = 84 × 63
Since the GCF of 84 and 63 = 21
⇒ 21 × LCM(84, 63) = 5292
Therefore, LCM = 252
☛ GCF Calculator
What are the Methods to Find GCF of 63 and 84?
There are three commonly used methods to find the GCF of 63 and 84.
 By Euclidean Algorithm
 By Prime Factorization
 By Long Division
What is the Relation Between LCM and GCF of 63, 84?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 63 and 84, i.e. GCF × LCM = 63 × 84.
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