What are the factors of 34?

Apr 3, 2016

$1 , 2 , 17 \mathmr{and} 34$

Explanation:

By definition, $a$ is a factor of $b$, or $a | b$ iff and only if there exists an integer $k \in \mathbb{Z}$ such that $\frac{b}{a} = k \mathmr{and} b = k a$.
In other words, $\frac{b}{a}$ leaves a zero remainder.

In particular then, the factors of $34$ are all natural numbers that can divide into $34$ without leaving a remainder.
In other words, all $a$ such that $\frac{34}{a} \in \mathbb{Z}$.

So therefore the factors of $34$ are $1 , 2 , 17 , 34$.