## GCF of 9 and 12

The simplest way to find the greatest common factor (GCF) of 9 and 12 is by listing their factors and identifying the largest numbers common to both lists. The factors of 9 are 1, 3, and 9, while the factors of 12 are 1, 2, 3, 4, 6, and 12. The common factors shared by both numbers are 1 and 3, with 3 being the largest. Therefore, the GCF of 9 and 12 is 3. This method is direct and effective, especially for smaller numbers, allowing for a quick and clear determination of the greatest common divisor.

## GCF of 9 and 12

### GCF of 9 and 12 is 3.

## GCF of 9 and 12 by Prime Factorization Method.

To find the greatest common factor (GCF) of 9 and 12 using the prime factorization method:

**Step 1:** Prime factorize both numbers:

**For 9: **9 = 3²

**For 12:** 12 = 2² × 3

**Step 2: **Identify the common prime factors and their lowest powers:

The common prime factor between 9 and 12 is 3. The lowest power of 3 in both factorizations is 3¹.

**Step 3: **Multiply the common prime factors with their lowest powers to determine the GCF:

**GCF **= 3¹ = 3

Therefore, the greatest common factor (GCF) of 9 and 12 by prime factorization method is 3.

## GCF of 9 and 12 by Long Division Method.

To find the greatest common factor (GCF) of 9 and 12 using the long division method, follow these steps:

**Step 1: **Start by dividing the larger number (12) by the smaller number (9).

12 ÷ 9 = 1 with a remainder of 3.

**Step 2:** Then, take the divisor (9) and divide it by the remainder (3).

9 ÷ 3 = 3 with a remainder of 0.

Since the remainder is now 0, the division process stops here.

**Step 3: **The divisors at this step where the remainder becomes zero is the greatest common factor (GCF).

**GCF =** 3.

Therefore, the greatest common factor (GCF) of 9 and 12 by the long division method is 3.

## GCF of 9 and 12 by Listing Common Factors.

To find the greatest common factor (GCF) of 9 and 12 by listing common factors:

**Step 1:** List the factors of each number.

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

**Factors of 12**: 1, 2, 3, 4, 6, 12

**Step 2: **Identify the common factors.

**Common factors**: 1, 3

**Step 3:** Determine the greatest common factor.

The highest number in the list of common factors is **3**.

## How does understanding GCF benefit everyday decisions?

It aids in making decisions involving ratios, such as splitting ingredients or dividing tasks equally.

## Why might someone confuse the GCF with the LCM?

Because both involve finding commonalities between sets of numbers, though they serve different mathematical purposes.

## What if the GCF of 9 and 12 was wrongly calculated as 4?

This would be incorrect as 4 is not a factor of 9.

## What is the method to find the GCF using subtraction?

Continually subtract the smaller number from the larger until the numbers equal each other, revealing the GCF.

## Is there a quick method to find the GCF of small numbers like 9 and 12?

Listing common factors is typically the quickest method for small numbers.

## How many common factors do 9 and 12 have?

They have two common factors: 1 and 3.