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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 non-zero 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 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.

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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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