# 7/30 simplified

#### Understand the Problem

The question is asking to simplify the fraction 7/30. The approach involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number.

The simplified fraction is $\frac{7}{30}$.

The simplified fraction is $\frac{7}{30}$.

#### Steps to Solve

1. Identify the GCD of 7 and 30

To simplify the fraction, we first find the greatest common divisor (GCD) of the numerator (7) and the denominator (30).

The prime factorization of 7 is just 7 (since it's a prime number), and the prime factorization of 30 is $2 \times 3 \times 5$.

Since there are no common factors, the GCD of 7 and 30 is 1.

1. Divide by the GCD

Next, we simplify the fraction by dividing both the numerator and the denominator by the GCD.

[ \frac{7}{30} = \frac{7 \div 1}{30 \div 1} = \frac{7}{30} ]

1. State the simplified fraction

Since the GCD is 1, the fraction is already in its simplest form.

Thus, the simplified fraction remains:

[ \frac{7}{30} ]

The simplified fraction is $\frac{7}{30}$.

The fraction $\frac{7}{30}$ is in its simplest form as 7 and 30 have no common factors other than 1. This means that it cannot be simplified further.