QUICK ANSWER
"No" is a form of "no", an adverb which is often translated as "no". "El hecho de que" is a phrase which is often translated as "the fact that". Learn more about the difference between "el hecho de que" and "no" below.
el hecho de que(
ehl
eh
-
choh
deh
keh
)A phrase is a group of words commonly used together (e.g., once upon a time).
1. (general)
a. the fact that
A pesar del hecho de que la economía ha estado mejorando de manera sostenida, la pobreza sigue siendo elevada.Despite the fact that the economy has been steadily improving, poverty is still high.
no(
noh
)An adverb is a word that describes a verb, an adjective, or other adverbs (e.g., to run quickly, very tired).
1. (negation)
a. no
¿Te gustó el concierto? - No, ese estilo de música no me gusta.Did you like the concert? - No, I don't like that style of music.
c. non-
Una organización no gubernamental es una asociación que actúa con independencia del gobierno.A non-governmental organization is an association that operates independently from the government.
a. no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
Vamos a la fiesta esta noche ¿no?We're going to the party tonight, aren't we?
Firmaste el contrato ¿no?You signed the contract, didn't you?
a. no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
Deberíamos llamarlos ¿no?We should call them, shouldn't we?
Te acompaño ¿no?Why don't I come with you?
An interjection is a short utterance that expresses emotion, hesitation, or protest (e.g., Wow!).
a. no
Quiero que limpies tu cuarto ahora mismo. - ¡No!I want you to clean your room right now. - No!