GCF of 4 and 9
GCF of 4 and 9 is the largest possible number that divides 4 and 9 exactly without any remainder. The factors of 4 and 9 are 1, 2, 4 and 1, 3, 9 respectively. There are 3 commonly used methods to find the GCF of 4 and 9  long division, Euclidean algorithm, and prime factorization.
1.  GCF of 4 and 9 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 4 and 9?
Answer: GCF of 4 and 9 is 1.
Explanation:
The GCF of two nonzero integers, x(4) and y(9), is the greatest positive integer m(1) that divides both x(4) and y(9) without any remainder.
Methods to Find GCF of 4 and 9
The methods to find the GCF of 4 and 9 are explained below.
 Prime Factorization Method
 Long Division Method
 Using Euclid's Algorithm
GCF of 4 and 9 by Prime Factorization
Prime factorization of 4 and 9 is (2 × 2) and (3 × 3) respectively. As visible, there are no common prime factors between 4 and 9, i.e. they are coprime. Hence, the GCF of 4 and 9 will be 1.
GCF of 4 and 9 by Long Division
GCF of 4 and 9 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 9 (larger number) by 4 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (4) by the remainder (1).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 4 and 9.
GCF of 4 and 9 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 = 9 and Y = 4
 GCF(9, 4) = GCF(4, 9 mod 4) = GCF(4, 1)
 GCF(4, 1) = GCF(1, 4 mod 1) = GCF(1, 0)
 GCF(1, 0) = 1 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 4 and 9 is 1.
☛ Also Check:
 GCF of 26 and 52 = 26
 GCF of 70 and 21 = 7
 GCF of 42 and 60 = 6
 GCF of 26 and 39 = 13
 GCF of 68 and 34 = 34
 GCF of 56 and 21 = 7
 GCF of 25 and 40 = 5
GCF of 4 and 9 Examples

Example 1: The product of two numbers is 36. If their GCF is 1, what is their LCM?
Solution:
Given: GCF = 1 and product of numbers = 36
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 36/1
Therefore, the LCM is 36. 
Example 2: For two numbers, GCF = 1 and LCM = 36. If one number is 4, find the other number.
Solution:
Given: GCF (y, 4) = 1 and LCM (y, 4) = 36
∵ GCF × LCM = 4 × (y)
⇒ y = (GCF × LCM)/4
⇒ y = (1 × 36)/4
⇒ y = 9
Therefore, the other number is 9. 
Example 3: Find the greatest number that divides 4 and 9 exactly.
Solution:
The greatest number that divides 4 and 9 exactly is their greatest common factor, i.e. GCF of 4 and 9.
⇒ Factors of 4 and 9: Factors of 4 = 1, 2, 4
 Factors of 9 = 1, 3, 9
Therefore, the GCF of 4 and 9 is 1.
FAQs on GCF of 4 and 9
What is the GCF of 4 and 9?
The GCF of 4 and 9 is 1. To calculate the greatest common factor of 4 and 9, we need to factor each number (factors of 4 = 1, 2, 4; factors of 9 = 1, 3, 9) and choose the greatest factor that exactly divides both 4 and 9, i.e., 1.
What is the Relation Between LCM and GCF of 4, 9?
The following equation can be used to express the relation between LCM and GCF of 4 and 9, i.e. GCF × LCM = 4 × 9.
How to Find the GCF of 4 and 9 by Prime Factorization?
To find the GCF of 4 and 9, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 9 = 3 × 3.
⇒ There is no common prime factor for 4 and 9. Hence, GCF (4, 9) = 1.
☛ What are Prime Numbers?
If the GCF of 9 and 4 is 1, Find its LCM.
GCF(9, 4) × LCM(9, 4) = 9 × 4
Since the GCF of 9 and 4 = 1
⇒ 1 × LCM(9, 4) = 36
Therefore, LCM = 36
☛ GCF Calculator
How to Find the GCF of 4 and 9 by Long Division Method?
To find the GCF of 4, 9 using long division method, 9 is divided by 4. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 4 and 9?
There are three commonly used methods to find the GCF of 4 and 9.
 By Listing Common Factors
 By Long Division
 By Prime Factorization
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