which expression has both 8 and n as factors

Guri Bee

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21-10-2024

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Unlocking the Mystery: Finding Expressions with 8 and n as Factors

In the world of mathematics, factors are like building blocks. They're numbers that multiply together to form a larger number. Let's explore how to identify expressions that have both 8 and n as factors.

Understanding Factors

Imagine a number, say 12. Its factors are the numbers that divide evenly into it: 1, 2, 3, 4, 6, and 12.

Now, let's consider the variable n. We don't know its specific value, but we know that it's a factor in our expression. This means n must be able to divide evenly into our expression.

Building Expressions with 8 and n as Factors

To have both 8 and n as factors, our expression must be divisible by both numbers. Here's how we can approach this:

1. Multiplication: The most straightforward way is to multiply 8 and n:

   • 8 * n = 8n
   • This expression clearly has both 8 and n as factors.

2. Multiples of 8n: Any multiple of 8n will also have both 8 and n as factors.

   • For example, 2 * 8*n = 16n also has 8 and n as factors.

3. Introducing Other Factors: We can introduce additional factors, but they must be compatible with 8 and n.

   • For instance, 24n has 8 and n as factors (since 24 is a multiple of 8).

Practical Example: Geometry

Imagine you're building a rectangular garden with an area represented by the expression 8n square meters.

• 8n tells you that the garden has a length of 8 meters and a width of n meters.
• This means the garden's area is always a multiple of 8 and n.

Key Takeaways

• To have both 8 and n as factors, an expression must be divisible by both 8 and n.
• Multiplying 8 and n guarantees an expression with both factors.
• You can create more complex expressions with additional factors, but they must be multiples of 8 and/or n.

Remember:

• We use the term "factor" to describe a number or variable that divides evenly into a larger number or expression.
• In expressions, factors can be constants (like 8) or variables (like n).

By understanding the concept of factors, we can confidently identify and create expressions that fit specific conditions.