Question

Apply distributive property to factor out the greatest common factor for the numbers 30 and 48. show your work please.

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Answer 1

what is this ^

Answer 2

To factor out the greatest common factor (GCF) for the numbers 30 and 48, we first need to determine what their GCF is.

1. **Find the GCF of 30 and 48**:
- The prime factorization of 30 is:
\[
30 = 2 \times 3 \times 5
\]
- The prime factorization of 48 is:
\[
48 = 2^4 \times 3
\]
- The common prime factors are \(2\) and \(3\).
- The lowest power of \(2\) in both factorizations is \(2^1\) and for \(3\) it is \(3^1\).

Thus, the GCF is:
\[
GCF = 2^1 \times 3^1 = 2 \times 3 = 6
\]

2. **Apply the distributive property**:
- We can write both 30 and 48 as a multiple of their GCF:
\[
30 = 6 \times 5
\]
\[
48 = 6 \times 8
\]
- Now we can express them in a form that shows the GCF:
\[
30 + 48 = 6 \times 5 + 6 \times 8
\]

3. **Use the distributive property to factor out the GCF**:
\[
30 + 48 = 6(5 + 8)
\]

So, the final expression factoring out the greatest common factor is:
\[
6(5 + 8)
\]

This demonstrates the application of the distributive property by factoring out the GCF of 30 and 48.

Answer 3

The symbol `^` is used to denote exponentiation in mathematics. For example, \(2^3\) means \(2\) raised to the power of \(3\), which equals \(2 \times 2 \times 2 = 8\).

In the context of my previous response, I used it to indicate powers of numbers:

- \(2^4\) means \(2\) raised to the power of \(4\) (which equals \(16\)).
- \(2^1\) means \(2\) raised to the power of \(1\), which is simply \(2\).
- \(3^1\) means \(3\) raised to the power of \(1\), which is simply \(3\).

If you have any further questions or need clarification on anything else, feel free to ask!