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

You are watching: What is the greatest common factor of 3 and 9

1. | GCF of 3 and 9 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF of 3 and 9 is 3.

**Explanation: **

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

The methods to find the GCF of 3 and 9 are explained below.

Listing Common FactorsLong Division MethodPrime Factorization Method### GCF of 3 and 9 by Listing Common Factors

**Factors of 3:**1, 3

**Factors of 9:**1, 3, 9

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

### GCF of 3 and 9 by Long Division

GCF of 3 and 9 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

**Step 2:**Since the remainder = 0, the divisor (3) is the GCF of 3 and 9.

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

### GCF of 3 and 9 by Prime Factorization

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

**☛ Also Check:**

## GCF of 3 and 9 Examples

**Example 1: The product of two numbers is 27. If their GCF is 3, what is their LCM? **

**Solution:**

Given: GCF = 3 and product of numbers = 27∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 27/3Therefore, the LCM is 9.

**Example 2: Find the GCF of 3 and 9, if their LCM is 9. **

**Solution: **

∵ LCM × GCF = 3 × 9⇒ GCF(3, 9) = (3 × 9)/9 = 3Therefore, the greatest common factor of 3 and 9 is 3.

**Example 3: Find the greatest number that divides 3 and 9 exactly. **

**Solution: **

The greatest number that divides 3 and 9 exactly is their greatest common factor, i.e. GCF of 3 and 9.⇒ Factors of 3 and 9:

Factors of 3 = 1, 3Factors of 9 = 1, 3, 9Therefore, the GCF of 3 and 9 is 3.

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## FAQs on GCF of 3 and 9

### What is the GCF of 3 and 9?

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

### What are the Methods to Find GCF of 3 and 9?

There are three commonly used methods to find the **GCF of 3 and 9**.

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

GCF(9, 3) × LCM(9, 3) = 9 × 3Since the GCF of 9 and 3 = 3⇒ 3 × LCM(9, 3) = 27Therefore, LCM = 9☛ Greatest Common Factor Calculator

### What is the Relation Between LCM and GCF of 3, 9?

The following equation can be used to express the relation between Least Common Multiple and GCF of 3 and 9, i.e. GCF × LCM = 3 × 9.

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### How to Find the GCF of 3 and 9 by Long Division Method?

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

### How to Find the GCF of 3 and 9 by Prime Factorization?

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