How does the Euler Totient Function apply here?

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How many positive integers $< 2013$ are divisible by $2$

Can I somehow use Euler's Totient function to find this?

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As your problem is currently stated, you are asking how many even numbers there are less than $2013$. For integers less than $2013$ that are divisible by $3$,$5$ or a general prime $p$, I would just use the division algorithm to rewrite $2012 = qp+r$ where $q,r \in \Bbb{N} \cup \{0 \}$ and $r<p$. The number you are looking for is $q$.