# GCF of 9 and 15

Created by: Team Maths - Examples.com, Last Updated: May 29, 2024

## GCF of 9 and 15

To find the Greatest Common Factor (GCF) of 9 and 15, you can use several methods such as listing common factors, prime factorization, and the long division method. By listing the factors, we see that the numbers factors of 9 are 1, 3, and 9, while the factors of 15 are 1, 3, 5, and 15. The common factors are 1 and 3, with the greatest common factor being 3. Using the prime factorization method, 9 is 3² and 15 is 3 × 5, with the common prime factor being 3. Using the long division method, dividing 15 by 9 gives a remainder of 6, then dividing 9 by 6 gives a remainder of 3, and finally dividing 6 by 3 gives a remainder of 0, confirming that the GCF is 3. Thus, the GCF of 9 and 15 is 3.

## Methods to Find GCF of 9 and 15

1. Prime Factorization Method
2. Long Division Method
3. Listing Common Factors

## GCF of 9 and 15 by Prime Factorization Method.

To find the Greatest Common Factor (GCF) of 9 and 15 using the prime factorization method, follow these steps:

### Step 1: Find the prime factorization of each number

Prime factorization of 9:

9 = 3 × 3 = 3²

Prime factorization of 15:

15 = 3 × 5

### Step 2: Identify the common prime factors

The only common prime factor of 9 and 15 is 3.

### Step 3: Multiply the common prime factors

Since the only common prime factor is 3, the GCF is 3.

## GCF of 9 and 15 by Long Division Method.

To find the Greatest Common Factor (GCF) of 9 and 15 using the long division method, follow these steps:

### Step 1: Divide the larger number by the smaller number

15 ÷ 9 = 1 with a remainder of 6.

### Step 2: Replace the larger number with the smaller number, and the smaller number with the remainder

Now, we have 9 and 6.

### Step 3: Repeat the division

9 ÷ 6 = 1 with a remainder of 3.

### Step 4: Continue the process

6 ÷ 3 = 2 with a remainder of 0.

### Step 5: When the remainder is 0, the divisors is the GCF

The last non-zero remainder is 3. So, the GCF of 9 and 15 is 3.

## GCF of 9 and 15 by Listing Common Factors.

To find the Greatest Common Factor (GCF) of 9 and 15 by listing common factors, follow these steps:

Factors of 9:

1, 3, 9

Factors of 15:

1, 3, 5, 15

### Step 2: Identify the common factors

Common factors of 9 and 15:

1, 3

### Step 3: Determine the greatest common factor

The largest common factor is 3. Therefore, the GCF of 9 and 15 is 3.

## How do you find the GCF of 9 and 15?

Use methods like long division, listing common factors, and prime factorization.

## What are the factors of 9?

The factors of 9 are 1, 3, and 9.

## How does the GCF help in simplifying fractions?

The GCF can be used to divide both the numerator and the denominator to simplify a fraction.

## Is the GCF of 9 and 15 a prime number?

Yes, 3 is a prime number.

## Can the GCF of 9 and 15 be one of the numbers?

Yes, if one number is a multiple of the other. For 9 and 15, the GCF is 3.

## What is the least common multiple (LCM) of 9 and 15?

The LCM of 9 and 15 is 45.

## Are 9 and 15 relatively prime?

No, because their GCF is 3, not 1.

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