Find the gcf of 12 24 36 with the real computation of it

To find the greatest common factor (GCF) of 12, 24, and 36 using the prime factorization method, we follow these steps:

### Step 1: Find the Prime Factorization of Each Number

- **Prime factorization of 12**:
  - \( 12 = 2^2 \times 3 \)

- **Prime factorization of 24**:
  - \( 24 = 2^3 \times 3 \)

- **Prime factorization of 36**:
  - \( 36 = 2^2 \times 3^2 \)

### Step 2: Identify the Common Prime Factors

Now, we identify the common prime factors in each of the numbers:

- For 12: \( 2^2 \times 3 \)
- For 24: \( 2^3 \times 3 \)
- For 36: \( 2^2 \times 3^2 \)

The common prime factors are \(2\) and \(3\).

### Step 3: Choose the Lowest Power of Each Common Factor

- The lowest power of 2 is \(2^2\).
- The lowest power of 3 is \(3\).

### Step 4: Multiply the Lowest Powers

The GCF is the product of these lowest powers:
\[ 
GCF = 2^2 \times 3 = 4 \times 3 = 12 
\]

Thus, the GCF of 12, 24, and 36 is **12**.

Would you like any further details or have any questions?

Here are 5 related questions you might consider:
1. How can the GCF of 12, 18, and 30 be found using prime factorization?
2. What is the least common multiple (LCM) of 12, 24, and 36?
3. How do you determine the GCF of two numbers using the Euclidean algorithm?
4. What is the GCF of 48, 72, and 96?
5. How does the GCF relate to simplifying fractions?

**Tip:** When finding the GCF using prime factorization, always choose the smallest exponent for each common prime factor.

Discover how to find the greatest common factor (GCF) of 12, 24, and 36 step-by-step with prime factorization. Learn about identifying common prime factors and calculating the GCF using the lowest powers. Suitable for Grades 6-8 students learning number theory and prime factorization.

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