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GCF of 9 and 33

GCF of 9 and 33 is the largest possible number that divides 9 and 33 exactly without any remainder. The factors of 9 and 33 are 1, 3, 9 and 1, 3, 11, 33 respectively. There are 3 commonly used methods to find the GCF of 9 and 33 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 9 and 33
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 33?

Answer: GCF of 9 and 33 is 3.

Explanation:

The GCF of two non-zero integers, x(9) and y(33), is the greatest positive integer m(3) that divides both x(9) and y(33) without any remainder.

Methods to Find GCF of 9 and 33

The methods to find the GCF of 9 and 33 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 9 and 33 by Listing Common Factors

Factors of 9: 1, 3, 9
Factors of 33: 1, 3, 11, 33

There are 2 common factors of 9 and 33, that are 1 and 3. Therefore, the greatest common factor of 9 and 33 is 3.

GCF of 9 and 33 by Prime Factorization

Prime factorization of 9 and 33 is (3 × 3) and (3 × 11) respectively. As visible, 9 and 33 have only one common prime factor i.e. 3. Hence, the GCF of 9 and 33 is 3.

GCF of 9 and 33 by Long Division

GCF of 9 and 33 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 33 (larger number) by 9 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 9 and 33.

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GCF of 9 and 33 Examples

Example 1: Find the GCF of 9 and 33, if their LCM is 99.

Solution:

∵ LCM × GCF = 9 × 33
⇒ GCF(9, 33) = (9 × 33)/99 = 3
Therefore, the greatest common factor of 9 and 33 is 3.
Example 2: For two numbers, GCF = 3 and LCM = 99. If one number is 33, find the other number.

Solution:

Given: GCF (x, 33) = 3 and LCM (x, 33) = 99
∵ GCF × LCM = 33 × (x)
⇒ x = (GCF × LCM)/33
⇒ x = (3 × 99)/33
⇒ x = 9
Therefore, the other number is 9.
Example 3: Find the greatest number that divides 9 and 33 exactly.

Solution:

The greatest number that divides 9 and 33 exactly is their greatest common factor, i.e. GCF of 9 and 33.
⇒ Factors of 9 and 33:
- Factors of 9 = 1, 3, 9
- Factors of 33 = 1, 3, 11, 33
Therefore, the GCF of 9 and 33 is 3.

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FAQs on GCF of 9 and 33

What is the GCF of 9 and 33?

The GCF of 9 and 33 is 3. To calculate the greatest common factor (GCF) of 9 and 33, we need to factor each number (factors of 9 = 1, 3, 9; factors of 33 = 1, 3, 11, 33) and choose the greatest factor that exactly divides both 9 and 33, i.e., 3.

How to Find the GCF of 9 and 33 by Long Division Method?

To find the GCF of 9, 33 using long division method, 33 is divided by 9. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 9, 33?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 9 and 33, i.e. GCF × LCM = 9 × 33.

If the GCF of 33 and 9 is 3, Find its LCM.

GCF(33, 9) × LCM(33, 9) = 33 × 9
Since the GCF of 33 and 9 = 3
⇒ 3 × LCM(33, 9) = 297
Therefore, LCM = 99
☛ Greatest Common Factor Calculator

How to Find the GCF of 9 and 33 by Prime Factorization?

To find the GCF of 9 and 33, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 33 = 3 × 11.
⇒ Since 3 is the only common prime factor of 9 and 33. Hence, GCF (9, 33) = 3.
☛ What is a Prime Number?

What are the Methods to Find GCF of 9 and 33?

There are three commonly used methods to find the GCF of 9 and 33.

By Euclidean Algorithm
By Long Division
By Prime Factorization

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