Math help

I want to take a cable section from a sweater and turn it into a hat. I was going to cast on 120 sts, when I planned it on paper it looked like it would work out by pulling 6 sts before starting each repeat in reality it isn’t coming together. I would prefer to do it in the round, but have done hats flat, I made a scarf in the pattern, so ideally I’d like to keep the pattern vertical like the scarf, but was wondering how weird it would look if I did the pattern horizontal.

What is the name of the sweater? It may help to see the cable.
What was causing the problem with knitting the cable vertically in the round as a hat?
You can certainly work the cable and some side sts then turn and use it as a horizontal section of the hat.
Here’s a single cable knit vertically as an example.

And here’s a horizontal cable.