Question

Using the greatest common factor, simplify the fraction 160200
(1 point)
Responses

45
4 fifths

1620
16 over 20

4050
40 over 50

40

Answer 1

To simplify the fraction \( \frac{160200}{4050} \) using the greatest common factor (GCF), we first need to find the GCF of the numerator and the denominator.

1. **Find the GCF of 160200 and 4050:**
- First, we can factor both numbers.

- **For 160200:**
- Prime factorization:
\[
160200 = 1602 \times 100 = 1602 \times (10 \times 10)
\]
- breaking down 1602:
\[
1602 = 2 \times 801
\]
\[
801 = 3 \times 267
\]
\[
267 = 3 \times 89
\]
Thus, \( 160200 = 2^1 \times 3^2 \times 5^2 \times 89^1\).

- **For 4050:**
- Prime factorization:
\[
4050 = 405 \times 10
\]
- breaking down 405:
\[
405 = 3 \times 135
\]
\[
135 = 3 \times 45
\]
\[
45 = 3^2 \times 5
\]
Thus, \( 4050 = 2^1 \times 3^4 \times 5^1\).

2. **Now, find the GCF:**
- The GCF is found by taking the lowest power of each common prime factor:
- From \( 2\): minimum power is \( 1\)
- From \( 3\): minimum power is \( 2\)
- From \( 5\): minimum power is \( 1\)

So, \( \text{GCF} = 2^1 \times 3^2 \times 5^1 = 2 \times 9 \times 5 = 90\).

3. **Divide both by GCF to simplify:**
- Now, divide the numerator and denominator of the fraction by their GCF (90):
\[
\frac{160200 \div 90}{4050 \div 90} = \frac{1780}{45}
\]

Thus, the simplified form of the fraction \( \frac{160200}{4050} \) is:

**Answer: 1780 over 45 (not listed among the options). Please verify if the original values were listed correctly.**