My guess is that you're talking about the Battle of Thermopylae. The Persians lost about 20,000 men, but there weren't "300 Greeks" ... there were 300 Spartans, in a mixed force totaling around 7,000 Greeks in all. They managed to hold off the Persian army for around a week, including two days of actual fighting.
When the (much larger) Persian army found a way around the narrow pass to outflank the Greeks, the Spartan general Leonidas and a force of about 300 Spartans (and around 1200 other Greeks from various cities) remained to hold off the Persians while the bulk of the Greek force escaped to warn the cities of Greece that the Persians had taken the pass and were on their way. This rear guard was essentially annihilated on the third day of fighting. All told, the Greeks lost between 2,000 and 4,000 men in the battle.
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