GCF of 63 and 72
GCF of 63 and 72 is the largest possible number that divides 63 and 72 exactly without any remainder. The factors of 63 and 72 are 1, 3, 7, 9, 21, 63 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 63 and 72  long division, Euclidean algorithm, and prime factorization.
1.  GCF of 63 and 72 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 63 and 72?
Answer: GCF of 63 and 72 is 9.
Explanation:
The GCF of two nonzero integers, x(63) and y(72), is the greatest positive integer m(9) that divides both x(63) and y(72) without any remainder.
Methods to Find GCF of 63 and 72
The methods to find the GCF of 63 and 72 are explained below.
 Prime Factorization Method
 Long Division Method
 Using Euclid's Algorithm
GCF of 63 and 72 by Prime Factorization
Prime factorization of 63 and 72 is (3 × 3 × 7) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 63 and 72 have common prime factors. Hence, the GCF of 63 and 72 is 3 × 3 = 9.
GCF of 63 and 72 by Long Division
GCF of 63 and 72 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 72 (larger number) by 63 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (63) by the remainder (9).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (9) is the GCF of 63 and 72.
GCF of 63 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 = 63
 GCF(72, 63) = GCF(63, 72 mod 63) = GCF(63, 9)
 GCF(63, 9) = GCF(9, 63 mod 9) = GCF(9, 0)
 GCF(9, 0) = 9 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 63 and 72 is 9.
☛ Also Check:
 GCF of 36 and 49 = 1
 GCF of 18 and 28 = 2
 GCF of 18 and 45 = 9
 GCF of 9 and 30 = 3
 GCF of 21 and 49 = 7
 GCF of 21 and 42 = 21
 GCF of 40 and 72 = 8
GCF of 63 and 72 Examples

Example 1: The product of two numbers is 4536. If their GCF is 9, what is their LCM?
Solution:
Given: GCF = 9 and product of numbers = 4536
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 4536/9
Therefore, the LCM is 504. 
Example 2: For two numbers, GCF = 9 and LCM = 504. If one number is 63, find the other number.
Solution:
Given: GCF (x, 63) = 9 and LCM (x, 63) = 504
∵ GCF × LCM = 63 × (x)
⇒ x = (GCF × LCM)/63
⇒ x = (9 × 504)/63
⇒ x = 72
Therefore, the other number is 72. 
Example 3: Find the GCF of 63 and 72, if their LCM is 504.
Solution:
∵ LCM × GCF = 63 × 72
⇒ GCF(63, 72) = (63 × 72)/504 = 9
Therefore, the greatest common factor of 63 and 72 is 9.
FAQs on GCF of 63 and 72
What is the GCF of 63 and 72?
The GCF of 63 and 72 is 9. To calculate the greatest common factor of 63 and 72, we need to factor each number (factors of 63 = 1, 3, 7, 9, 21, 63; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 63 and 72, i.e., 9.
What is the Relation Between LCM and GCF of 63, 72?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 63 and 72, i.e. GCF × LCM = 63 × 72.
How to Find the GCF of 63 and 72 by Long Division Method?
To find the GCF of 63, 72 using long division method, 72 is divided by 63. The corresponding divisor (9) when remainder equals 0 is taken as GCF.
How to Find the GCF of 63 and 72 by Prime Factorization?
To find the GCF of 63 and 72, we will find the prime factorization of the given numbers, i.e. 63 = 3 × 3 × 7; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 63 and 72. Hence, GCF(63, 72) = 3 × 3 = 9
☛ What are Prime Numbers?
What are the Methods to Find GCF of 63 and 72?
There are three commonly used methods to find the GCF of 63 and 72.
 By Prime Factorization
 By Long Division
 By Listing Common Factors
If the GCF of 72 and 63 is 9, Find its LCM.
GCF(72, 63) × LCM(72, 63) = 72 × 63
Since the GCF of 72 and 63 = 9
⇒ 9 × LCM(72, 63) = 4536
Therefore, LCM = 504
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