To simplify the expression \(\frac{916}{81}\), we need to find the greatest common divisor (GCD) of 916 and 81 and then divide both the numerator and the denominator by their GCD.
First, let's find the GCD of 916 and 81. We can use the Euclidean algorithm to do this.
1. Divide 916 by 81 and find the remainder:
\( 916 \div 81 \approx 11 \) with a remainder of \( 916 - 81 \times 11 = 916 - 891 = 25 \).
2. Now take 81 and 25, and apply the algorithm again:
\( 81 \div 25 \approx 3 \) with a remainder of \( 81 - 25 \times 3 = 81 - 75 = 6 \).
3. Take 25 and 6, and apply the algorithm again:
\( 25 \div 6 \approx 4 \) with a remainder of \( 25 - 6 \times 4 = 25 - 24 = 1 \).
4. Finally, take 6 and 1:
\( 6 \div 1 = 6 \) with a remainder of \( 6 - 1 \times 6 = 0 \).
Since the remainder is now 0, the last non-zero remainder is 1, which means the GCD of 916 and 81 is 1.
Since the GCD is 1, \(\frac{916}{81}\) is already in its simplest form.
So, the simplified expression is:
\[ \frac{916}{81} \]
6.
Simplify the expression.
916
81
1 answer