# Prove that the fraction (21n+4)/(14n+3) is irreducible for every n in NN?

Nov 10, 2016

Calculate the GCF of $21 n + 4$ and $14 n + 3$, finding that it is $1$

#### Explanation:

Calculate the GCF of $21 n + 4$ and $14 n + 3$:

$\frac{21 n + 4}{14 n + 3} = 1 \text{ }$ with remainder $7 n + 1$

$\frac{14 n + 3}{7 n + 1} = 2 \text{ }$ with remainder $1$

$\frac{7 n + 1}{1} = 7 n + 1 \text{ }$ with remainder $0$

So the GCF is $1$