They're both Germanic languages, just like Dutch, German, Norwegian, Danish and a few others. Same origin. All of them have variations of tre/dre/drei/thir/þre/þrēo (say them with sounds halfway between t and d as the first sound, and you'll see how similar they are) followed by variations of ten/teen/tin/tan/ton/tien/zehn as a suffix for ten (again, pick a halfway point between t and z and it's easier to see how similar they are).

In Old English it was þrēotīene ( þ is "th"), and in Old Norse it was þrettán, same as modern Icelandic, so the first common root is even further back, but you can see the similarity. The *hypothesized proto-Germanic root is þritehun. (þriz + tehun.

But, it goes back even further than that. The Romance languages (tres, trois etc) shares the same proto-Indo-European root (hypothesized to be tréyes) for three with proto-Germanic.

The names for numbers are ancient, and though not always recognisable, sometimes recognizable variants pop up even further away than you'd expect. E.g. Pashto (Southeastern Iran) has dre for three, Sanskrit has trí, Indonesian has tri, all of them descendants of the same proto-Indo-European root.