It's an interesting way. I don't like the ternary operator thing personally, but some good ideas.

What I personally try to do, as a starting point

• If 'then' returns or throws at the end, there's no need for 'else', it's just code that happens after this early exit.
• If 'else' returns but 'then' doesn't, invert the condition, then do the above.

Both the flipping and the unwrapping of 'else' can be done by the IDE. This leaves:

const theFactorText = (number) => {
    if (number % 2 === 0) {
        return "Not the factor"
    }
    if (number % 5 === 0) {
        return "That's the factor"
    }
    if (number < 10) {
        return "Not the factor"
    }
    throw new Error(
        "Number doesn't fall under any category. Input another"
    )
}