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Step 1:I'll solve this step-by-step using the specified LaTeX formatting guidelines:
Step 2:: Identify the Greatest Common Factor (GCF)
- 36 = $$2^{2} \times 3^{2}
To simplify a fraction, we need to find the largest number that divides both the numerator and denominator evenly. Let's factor both numbers:
Step 3:: Determine the Common Factors
Looking at the prime factorizations, we can see that $$3^{2}$$ is the largest common factor.
Step 4:: Divide Both Numerator and Denominator by the GCF
- Numerator: $$27 \div (3^{2}) = 3
- Denominator: 36 \div (3^{2}) = 12
Step 5:: Rewrite the Simplified Fraction
\frac{27}{36} = \frac{3}{12} = \frac{1}{4}
Final Answer
\frac{1}{4}
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