**What’s the secret to finding the greatest common factor of 42 and 96? Let’s explore the fascinating world of numbers and discover the magic behind it!**

If you’ve ever struggled to find the greatest common factor of two numbers, you’re not alone. It can be a tricky concept to grasp, but with a little guidance, you’ll be able to master this mathematical challenge.

**The greatest common factor (GCF) of two numbers is the largest number that divides both numbers evenly, with no remainder.** In other words, it’s the “greatest” factor that they have in common. So, what is the GCF of 42 and 96?

To find the GCF, we need to prime factorize both numbers:

- 42 = 2 x 3 x 7
- 96 = 2 x 2 x 2 x 2 x 2 x 3

The greatest common factor is the product of all the common prime factors, which in this case is:

**GCF = 2 x 3 = 6**

So, the greatest common factor of 42 and 96 is 6. This means that 6 is the largest number that can divide both 42 and 96 without leaving a remainder.

Now that you know the secret to finding the GCF, you can confidently approach any GCF problem that comes your way. Remember, it’s all about finding the greatest common factor that divides both numbers evenly. With a little practice, you’ll become a master number wizard!

## Determining the Greatest Common Factor (GCF) of 42 and 96

### Introduction

In mathematics, the greatest common factor (GCF) of two or more numbers represents the largest number that evenly divides all the given numbers without leaving a remainder. To find the GCF of 42 and 96, we can employ various techniques.

### Method 1: Prime Factorization

**Step 1: Decompose into Prime Factors**

- 42 = 2 x 3 x 7
- 96 = 2 x 2 x 2 x 2 x 2 x 3

**Step 2: Identify Common Prime Factors**

Both 42 and 96 share the prime factors 2 and 3.

**Step 3: Determine the GCF**

The GCF is the product of the common prime factors. Therefore, the GCF of 42 and 96 is:

```
GCF = 2 x 3 = 6
```

### Method 2: Euclidean Algorithm

**Step 1: Divide the Larger Number by the Smaller Number**

```
96 ÷ 42 = 2 (remainder 12)
```

**Step 2: Repeat Division with Remainder**

```
42 ÷ 12 = 3 (remainder 6)
```

```
12 ÷ 6 = 2 (remainder 0)
```

**Step 3: Determine the Last Non-Zero Remainder**

The last non-zero remainder is 6.

**Step 4: GCF is the Last Non-Zero Remainder**

Therefore, the GCF of 42 and 96 is:

```
GCF = 6
```

### Conclusion

Using either the prime factorization method or the Euclidean algorithm, we have determined that the greatest common factor of 42 and 96 is **6**.

### FAQs

**Q1: What is the GCF of 42 and 63?**

A: 21

**Q2: How can I find the GCF of three or more numbers?**

A: Find the GCF of any two numbers first, then find the GCF of that result and the third number.

**Q3: Why is the GCF useful?**

A: The GCF helps simplify fractions, equations, and other mathematical operations.

**Q4: Is there a formula to calculate the GCF?**

A: No, there is no direct formula for the GCF. However, the prime factorization and Euclidean algorithm methods provide efficient ways to find it.

**Q5: Can the GCF of two numbers be 1?**

A: Yes, the GCF of two numbers is 1 if they have no common factors other than 1.

.

What,Greatest,Common,Factor