GCF of 9 and 72
GCF of 9 and 72 is the largest possible number that divides 9 and 72 exactly without any remainder. The factors of 9 and 72 are 1, 3, 9 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 9 and 72  Euclidean algorithm, prime factorization, and long division.
1.  GCF of 9 and 72 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 9 and 72?
Answer: GCF of 9 and 72 is 9.
Explanation:
The GCF of two nonzero integers, x(9) and y(72), is the greatest positive integer m(9) that divides both x(9) and y(72) without any remainder.
Methods to Find GCF of 9 and 72
The methods to find the GCF of 9 and 72 are explained below.
 Prime Factorization Method
 Long Division Method
 Listing Common Factors
GCF of 9 and 72 by Prime Factorization
Prime factorization of 9 and 72 is (3 × 3) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 9 and 72 have common prime factors. Hence, the GCF of 9 and 72 is 3 × 3 = 9.
GCF of 9 and 72 by Long Division
GCF of 9 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 9 (smaller number).
 Step 2: Since the remainder = 0, the divisor (9) is the GCF of 9 and 72.
The corresponding divisor (9) is the GCF of 9 and 72.
GCF of 9 and 72 by Listing Common Factors
 Factors of 9: 1, 3, 9
 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
There are 3 common factors of 9 and 72, that are 1, 3, and 9. Therefore, the greatest common factor of 9 and 72 is 9.
☛ Also Check:
 GCF of 12 and 16 = 4
 GCF of 12 and 27 = 3
 GCF of 16 and 64 = 16
 GCF of 24 and 42 = 6
 GCF of 56 and 21 = 7
 GCF of 50 and 80 = 10
 GCF of 10 and 25 = 5
GCF of 9 and 72 Examples

Example 1: The product of two numbers is 648. If their GCF is 9, what is their LCM?
Solution:
Given: GCF = 9 and product of numbers = 648
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 648/9
Therefore, the LCM is 72. 
Example 2: Find the GCF of 9 and 72, if their LCM is 72.
Solution:
∵ LCM × GCF = 9 × 72
⇒ GCF(9, 72) = (9 × 72)/72 = 9
Therefore, the greatest common factor of 9 and 72 is 9. 
Example 3: Find the greatest number that divides 9 and 72 exactly.
Solution:
The greatest number that divides 9 and 72 exactly is their greatest common factor, i.e. GCF of 9 and 72.
⇒ Factors of 9 and 72: Factors of 9 = 1, 3, 9
 Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the GCF of 9 and 72 is 9.
FAQs on GCF of 9 and 72
What is the GCF of 9 and 72?
The GCF of 9 and 72 is 9. To calculate the greatest common factor (GCF) of 9 and 72, we need to factor each number (factors of 9 = 1, 3, 9; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 9 and 72, i.e., 9.
What are the Methods to Find GCF of 9 and 72?
There are three commonly used methods to find the GCF of 9 and 72.
 By Prime Factorization
 By Long Division
 By Listing Common Factors
If the GCF of 72 and 9 is 9, Find its LCM.
GCF(72, 9) × LCM(72, 9) = 72 × 9
Since the GCF of 72 and 9 = 9
⇒ 9 × LCM(72, 9) = 648
Therefore, LCM = 72
☛ GCF Calculator
How to Find the GCF of 9 and 72 by Long Division Method?
To find the GCF of 9, 72 using long division method, 72 is divided by 9. The corresponding divisor (9) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 9, 72?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 9 and 72, i.e. GCF × LCM = 9 × 72.
How to Find the GCF of 9 and 72 by Prime Factorization?
To find the GCF of 9 and 72, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 9 and 72. Hence, GCF(9, 72) = 3 × 3 = 9
☛ What is a Prime Number?
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