# How do you simplify the fraction 30/41?

$\frac{30}{41}$ is simplified because 41 is prime

#### Explanation:

This fraction can't be simplified any further than where it is. The reason is that the denominator is prime (which means there are no factors for it other than itself and one).

If the fraction had been, for example, $\frac{30}{42}$, we could factor it out this way:

$\frac{30}{42} = \frac{2 \times 15}{2 \times 21} = \frac{2 \times 3 \times 5}{2 \times 3 \times 7} = \left(\frac{2}{2}\right) \left(\frac{3}{3}\right) \left(\frac{5}{7}\right) = \frac{5}{7}$

but we can do that with the number 41.