find the GCF of 45 in  60 using prime factorzation

To find the greatest common factor (GCF) of 45 and 60 using prime factorization, follow these steps:

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

- **45**:  
  \( 45 = 3 \times 3 \times 5 = 3^2 \times 5 \)

- **60**:  
  \( 60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5 \)

### Step 2: Identify the common prime factors.

The prime factors of **45** are \( 3^2 \times 5 \).  
The prime factors of **60** are \( 2^2 \times 3 \times 5 \).

The common prime factors between 45 and 60 are **3** and **5**.

### Step 3: Choose the lowest powers of the common prime factors.

- The lowest power of 3 is \( 3^1 \).
- The lowest power of 5 is \( 5^1 \).

### Step 4: Multiply the common factors.

So, the GCF is:
\[
GCF = 3^1 \times 5^1 = 3 \times 5 = 15
\]

Thus, the greatest common factor (GCF) of 45 and 60 is **15**.

Would you like further details on this process or explanations?

Here are some related questions for further practice:
1. What is the GCF of 72 and 90 using prime factorization?
2. Find the GCF of 56 and 98 using the same method.
3. How would you use the Euclidean algorithm to find the GCF of 45 and 60?
4. What is the least common multiple (LCM) of 45 and 60?
5. How does the GCF help in simplifying fractions like \( \frac{45}{60} \)?

**Tip**: The GCF is useful in reducing fractions to their simplest form by dividing both the numerator and denominator by the GCF.

find the GCF of 45 in 60 using prime factorzation

Learn how to find the greatest common factor (GCF) of 45 and 60 using prime factorization. This step-by-step guide explores key number theory concepts, including prime factorization and GCF. Suitable for students in Grades 5-7.

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