72/65 simplified
Understand the Problem
The question is asking for the simplification of the fraction 72/65. This involves finding the greatest common divisor (GCD) of 72 and 65 and dividing both the numerator and denominator by that number.
Answer
The simplified form is $\frac{72}{65}$.
Answer for screen readers
The simplified form of the fraction is $\frac{72}{65}$.
Steps to Solve
- Find the GCD of 72 and 65
To simplify the fraction $\frac{72}{65}$, we first need to determine the greatest common divisor (GCD) of 72 and 65. The GCD is found by identifying the largest number that divides both numbers without a remainder.
The prime factors of 72 are $2^3 \cdot 3^2$ and the factors of 65 are $5 \cdot 13$. Since there are no common factors, the GCD is 1.
- Divide both the numerator and denominator by the GCD
Now that we know the GCD is 1, we can divide both the numerator and the denominator by 1 (which doesn’t change the values).
$$ \frac{72 \div 1}{65 \div 1} = \frac{72}{65} $$
- Conclude the simplification
Since the GCD is 1 and dividing by 1 does not simplify the fraction further, the fraction $\frac{72}{65}$ is already in its simplest form.
The simplified form of the fraction is $\frac{72}{65}$.
More Information
In this case, the fraction $\frac{72}{65}$ cannot be simplified further since the GCD is 1. It is an improper fraction, meaning the numerator (72) is greater than the denominator (65).
Tips
One common mistake is assuming that the GCD is not 1 and trying to reduce the fraction without checking the GCD, which can lead to incorrect simplification. Always find the GCD first!
