Kortnummeret og kontrolcifrene står på kortet.

Because Danish usually writes compound nouns as a single word.

So:

• kort = card
• nummer = number
• kortnummer = card number
• kortnummeret = the card number

The definite ending is added to the whole compound, not written separately. So kortnummeret is correct, while kort nummeret is not.

This is very common in Danish:

• telefonnummer = phone number
• adgangskode = password
• betalingskort = payment card

These are definite endings, attached to the noun.

• -et = definite singular for many neuter nouns
• -ne = definite plural

So in this sentence:

• kortnummeret = the card number
• kontrolcifrene = the check digits / control digits
• kortet = the card

Unlike English, Danish often puts the at the end of the noun instead of using a separate word.

Because Danish normally expresses definiteness with a suffix on the noun.

Compare:

• et kort = a card

• kortet = the card

• et nummer = a number

• nummeret = the number

• et kontrolciffer = a check digit
• kontrolcifrene = the check digits

A separate definite word such as det or den is usually used when there is an adjective:

• kortet = the card
• det nye kort = the new card

So in your sentence, no separate the is needed.

The dictionary form is et kontrolciffer.

Its forms are:

• et kontrolciffer = a check digit
• kontrolcifferet = the check digit
• kontrolcifre = check digits
• kontrolcifrene = the check digits

So kontrolcifrene is the definite plural form.

Because ciffer has the plural cifre in Danish. This is just the normal plural pattern for that noun.

So:

• et ciffer = a digit
• cifre = digits

And in the compound:

• et kontrolciffer
• kontrolcifre

This is something you mostly just learn as part of the noun’s forms.

Yes, står literally means stands, but in Danish it is also commonly used for information that is written, printed, or shown somewhere.

So står på kortet means something like:

• is on the card
• is written on the card
• appears on the card

This is very natural Danish. For example:

• Der står dit navn på brevet. = Your name is on the letter / written on the letter.
• Hvad står der på skiltet? = What does the sign say?

So here står is not about physically standing upright. It is about written information being present.

Yes, that would be understandable, and it is not grammatically wrong.

But står på kortet is often more natural when talking about text, numbers, or information printed on a physical object. It specifically suggests that the card number and check digits are written there.

So:

• er på kortet = are on the card
• står på kortet = are written/shown on the card

The version with står is usually the more idiomatic choice here.

Because Danish verbs do not change form according to singular or plural subjects in the present tense.

English has:

• it stands
• they stand

Danish just has:

• det står
• de står

So even though kortnummeret og kontrolcifrene is a plural subject, the verb is still simply står.

The basic structure is:

Subject + verb + prepositional phrase

• Kortnummeret og kontrolcifrene = subject
• står = verb
• på kortet = prepositional phrase

So the sentence is very straightforward.

Also, Danish is a V2 language, which means the finite verb normally comes in second position in main clauses. In this sentence, the subject comes first, so the verb naturally comes right after it.

På means on.

So på kortet means on the card. This is the natural preposition when something is printed on the surface of a card.

Examples:

• navnet står på kortet = the name is on the card
• nummeret står på bagsiden = the number is on the back

So på kortet is just the normal way to say that the information appears on the card itself.