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GCF of 9 and 30

GCF of 9 and 30 is the largest possible number that divides 9 and 30 exactly without any remainder. The factors of 9 and 30 are 1, 3, 9 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 9 and 30 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 9 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 30?

Answer: GCF of 9 and 30 is 3.

Explanation:

The GCF of two non-zero integers, x(9) and y(30), is the greatest positive integer m(3) that divides both x(9) and y(30) without any remainder.

Methods to Find GCF of 9 and 30

The methods to find the GCF of 9 and 30 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 9 and 30 by Prime Factorization

Prime factorization of 9 and 30 is (3 × 3) and (2 × 3 × 5) respectively. As visible, 9 and 30 have only one common prime factor i.e. 3. Hence, the GCF of 9 and 30 is 3.

GCF of 9 and 30 by Long Division

GCF of 9 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (larger number) by 9 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 9 and 30.

GCF of 9 and 30 by Listing Common Factors

Factors of 9: 1, 3, 9
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 2 common factors of 9 and 30, that are 1 and 3. Therefore, the greatest common factor of 9 and 30 is 3.

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GCF of 9 and 30 Examples

Example 1: For two numbers, GCF = 3 and LCM = 90. If one number is 30, find the other number.

Solution:

Given: GCF (z, 30) = 3 and LCM (z, 30) = 90
∵ GCF × LCM = 30 × (z)
⇒ z = (GCF × LCM)/30
⇒ z = (3 × 90)/30
⇒ z = 9
Therefore, the other number is 9.
Example 2: Find the greatest number that divides 9 and 30 exactly.

Solution:

The greatest number that divides 9 and 30 exactly is their greatest common factor, i.e. GCF of 9 and 30.
⇒ Factors of 9 and 30:
- Factors of 9 = 1, 3, 9
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 9 and 30 is 3.
Example 3: The product of two numbers is 270. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 270
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 270/3
Therefore, the LCM is 90.

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FAQs on GCF of 9 and 30

What is the GCF of 9 and 30?

The GCF of 9 and 30 is 3. To calculate the GCF of 9 and 30, we need to factor each number (factors of 9 = 1, 3, 9; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 9 and 30, i.e., 3.

How to Find the GCF of 9 and 30 by Long Division Method?

To find the GCF of 9, 30 using long division method, 30 is divided by 9. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

How to Find the GCF of 9 and 30 by Prime Factorization?

To find the GCF of 9 and 30, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 30 = 2 × 3 × 5.
⇒ Since 3 is the only common prime factor of 9 and 30. Hence, GCF (9, 30) = 3.
☛ What are Prime Numbers?

What are the Methods to Find GCF of 9 and 30?

There are three commonly used methods to find the GCF of 9 and 30.

By Prime Factorization
By Long Division
By Euclidean Algorithm

If the GCF of 30 and 9 is 3, Find its LCM.

GCF(30, 9) × LCM(30, 9) = 30 × 9
Since the GCF of 30 and 9 = 3
⇒ 3 × LCM(30, 9) = 270
Therefore, LCM = 90
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What is the Relation Between LCM and GCF of 9, 30?

The following equation can be used to express the relation between LCM and GCF of 9 and 30, i.e. GCF × LCM = 9 × 30.

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