Question

Complete the statements.
The
GCF of the numerator and denominator of
16/72 is
After dividing the numerator and denominator of
16/72 by their GCF, the resulting fraction,

equivalent to
16/72, rewritten in simplest form.

Answer 1

To find the GCF (Greatest Common Factor) of the numerator and denominator of \( \frac{16}{72} \):

1. **Find the prime factorization**:
- **16**: \( 16 = 2^4 \)
- **72**: \( 72 = 2^3 \times 3^2 \)

2. **Identify the common factors**:
- The common factor of 16 and 72 is \( 2 \), and the minimum exponent for \( 2 \) between the two factorizations is \( 3 \) (from 72).

3. **Calculate the GCF**:
- Thus, \( \text{GCF} = 2^3 = 8 \).

So, the GCF of the numerator and denominator of \( \frac{16}{72} \) is **8**.

Next, after dividing the numerator and denominator by their GCF:

- **Divide the numerator and denominator**:
\[
\frac{16 \div 8}{72 \div 8} = \frac{2}{9}
\]

Therefore, the resulting fraction, equivalent to \( \frac{16}{72} \), rewritten in simplest form is \( \frac{2}{9} \).

In summary:
- The GCF of the numerator and denominator of \( \frac{16}{72} \) is **8**.
- After dividing \( \frac{16}{72} \) by their GCF, the resulting fraction in simplest form is **\( \frac{2}{9} \)**.