שְׁלֹשׁ מְאוֹת, שְׁלֹשֶׁת אֲלָפִים
The Hebrew word for hundred is feminine, as its ah ending hints – מֵאָה
And since numbers are adjectives, three hundred is שְׁלֹשׁ מְאוֹת
– literally, three of hundred.
For example:
מִבְחַן נְהִיגָה בְּיִשְׂרָאֵל עוֹלֶה שְׁלֹשׁ מְאוֹת שְׁקָלִים!
A driving test in Israel costs three hundred shekels!
However, the word for thousand – אֶלֶף
– is masculine. Thus three thousand is שְׁלֹשֶׁת אֲלָפִים
– literally, three of thousand, as in:
קָנִיתִי מַחְשֵׁב בִּשְׁלֹשֶׁת אֲלָפִים שְׁקָלִים.
I bought a computer for three thousand shekels.
שלושת
is the construct form of the masculine version of Hebrew word for three – שְׁלֹשָׁה 
This may puzzle you, as the masculine שלושה has a feminine ah ending. That’s because numbers observe the opposite rule of other adjectives – the ah ending makes the number masculine, while the number without an ah ending is probably feminine – as in שלש מאות.