# Highest prime factor of factorial.

For a program I wrote, I used the property that the power of the highest prime factor of a factorial is always 1. I couldn't find anything about this, but it felt right. I can't prove it. Is my assumption correct or is it just a coincidence?

• What is the "last" prime factor of a factorial? – Christoph Oct 16 '15 at 12:28
• I meant the highest. Edited the question. – Nico Ekkart Oct 16 '15 at 12:30
• It's implied by the truth of Bertrand's postulate. – Daniel Fischer Oct 16 '15 at 12:30
• It's been proven that there is always a prime between $n$ and $2n$ for $n\ge2$. – dejongbrent Oct 16 '15 at 12:30