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.
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Find the GCF of 160200 and 4050:
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First, we can factor both numbers.
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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, \( 160200 = 2^1 \times 3^2 \times 5^2 \times 89^1\).
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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, \( 4050 = 2^1 \times 3^4 \times 5^1\).
- Prime factorization:
\[
4050 = 405 \times 10
\]
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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, \( \text{GCF} = 2^1 \times 3^2 \times 5^1 = 2 \times 9 \times 5 = 90\).
- The GCF is found by taking the lowest power of each common prime factor:
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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.
1 answer