The numbers ‘twenty’ to ‘ninety’ end in ‘-ty’.
Where does this part come from?

While it’s now a suffix, ‘-ty’ stems from a Proto-Germanic noun meaning “decade, a (group of) ten”.

For example, ‘forty’ comes from *fedwōr tegiwiz, literally “four tens”.

Only Icelandic, Swedish, and Elfdalian have preserved this word as a noun.

Click my new graphic to learn all about ‘-ty’ and its relatives:

@yvanspijk , my usual Finno-Ugric comments: the IE ‘10’ has, of course, been borrowed into Permic (Komi das) and Hungarian (tíz), from Iranian, two separate borrowings.
Then there is this nice tradition: from the 19th century on, scholars have tried to explain the second part of Finnish yhdeksän ‘9’ and kahdeksan ‘8’ as borrowings from IE ‘10’. (The first syllables in the Finnic numerals and their cognates in Saami, Mordvin and Mari obviously represent the numerals ‘1’ and ‘2’, and the motivation of the whole numeral would be something like ‘1 [or 2] missing from 10’.) The most recent version as formulated by Koivulehto and Parpola was based on the idea that the Proto-Iranian -ts- didn’t have a direct equivalent in Finno-Ugric (which only had a palatalized *ć and a broad *č) and was therefore substituted with -ks-. However, the vowels don’t match. Holopainen (2019) rejects this etymology and finds Erkki Itkonen’s old idea more convincing (albeit not flawless): these numerals would derive from *ükti / *kakti e-k-sä ‘1 (or 2) does not exist’.
But of course, as almost always, there's a more recent Swedish loanword: tjog ‘score’ has been borrowed into Finnish as tiu ‘20’ (used only when counting eggs).
@johanna_laakso Thank you very much for these interesting facts from a language family I've barrely touched the surface of.