**What is the GCF of h4 and h8?**

In mathematics, for two or more expressions, the greatest common factor (GCF) is the largest expression that is a factor of all the given expressions. Factors are expressions that can be multiplied together to get another expression. Finding the GCF can be useful for simplifying expressions and solving equations.

For the expressions h4 and h8, the GCF is h4. This is because h4 is a factor of both h4 and h8, and there is no other expression that is a factor of both h4 and h8 that is larger than h4.

In other words, the largest expression that can be multiplied by itself to get both h4 and h8 is h4.

## Greatest Common Factor (GCF)

In mathematics, the greatest common factor (GCF) of two or more integers is the largest positive integer that divides all those integers without leaving a remainder. It is also known as the **highest common factor (HCF)** or the **greatest common divisor (GCD)**.

### How to Find the GCF

There are several methods to find the GCF of two or more integers:

#### Prime Factorization

- Factor each integer into its prime factors.
- Identify the common prime factors and multiply them together.

**For example:**

To find the GCF of 12 and 18:

- Prime factors of 12: 2 x 2 x 3
- Prime factors of 18: 2 x 3 x 3
- Common prime factors: 2 x 3
- GCF: 6

#### Euclid’s Algorithm

- Divide the larger integer by the smaller integer.
- Divide the remainder by the divisor.
- Repeat steps 2 and 3 until the remainder is 0.
- The last non-zero remainder is the GCF.

**For example:**

To find the GCF of 24 and 36:

- 36 ÷ 24 = 1 remainder 12
- 24 ÷ 12 = 2 remainder 0
- GCF: 12

#### Using a Calculator

Many calculators have a built-in GCF function that can be used to find the GCF of two or more integers.

### GCF of H4 and H8

To find the GCF of H4 and H8:

**Step 1: Convert H4 and H8 to their decimal equivalents.**- H4 = 16
- H8 = 24

**Step 2: Find the prime factors of 16 and 24.**- Prime factors of 16: 2 x 2 x 2 x 2
- Prime factors of 24: 2 x 2 x 2 x 3

**Step 3: Identify the common prime factors and multiply them together.**- Common prime factors: 2 x 2 x 2
- GCF: 8

Therefore, the GCF of H4 and H8 is 8.

### Importance of GCF

The GCF has several important applications in mathematics, including:

**Simplifying fractions:**Dividing both the numerator and denominator of a fraction by their GCF simplifies the fraction to its lowest terms.**Solving equations:**The GCF is used to remove common factors from both sides of an equation, making it easier to solve.**Finding least common multiples (LCMs):**The GCF is used to find the LCM of two or more integers.**Solving divisibility problems:**The GCF can be used to determine if one integer is divisible by another.

## Additional Examples

- GCF of 10 and 15: 5
- GCF of 21 and 28: 7
- GCF of 32 and 48: 16
- GCF of 60 and 75: 15
- GCF of 81 and 126: 9

## Conclusion

The greatest common factor (GCF) is a fundamental mathematical concept used to find the largest common factor that divides two or more integers without leaving a remainder. It has numerous applications in mathematics, including simplifying fractions, solving equations, and finding least common multiples.

## Frequently Asked Questions (FAQs)

**What is the difference between GCF and LCM?**

- GCF is the largest common factor that divides two or more integers without leaving a remainder, while LCM is the smallest positive integer that is divisible by two or more integers.

**How do I find the GCF of three or more integers?**

- Find the GCF of two of the integers using one of the methods mentioned above. Then find the GCF of that result and the third integer. Repeat the process until you have included all the integers.

**Can the GCF of two integers be negative?**

- No, the GCF is always a positive integer.

**What is the GCF of any two consecutive integers?**

- 1

**What is the GCF of a number and 1?**

- The number itself

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