To evaluate \( \frac{52}{74} \) and simplify it completely, we first find the greatest common divisor (GCD) of 52 and 74.
The prime factorization of 52 is: \[ 52 = 2^2 \times 13 \]
The prime factorization of 74 is: \[ 74 = 2 \times 37 \]
The common factor is \( 2 \).
Now, we can divide both the numerator and the denominator by 2: \[ \frac{52 \div 2}{74 \div 2} = \frac{26}{37} \]
Since 26 and 37 have no common factors other than 1, \( \frac{26}{37} \) is in its simplest form.
Thus, the simplified answer to \( 52 \div 74 \) is: \[ \frac{26}{37} \]
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