Chacun/chacune/chaque = each one/each (French Indefinite Adjectives and Pronouns)

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Chacun/chacune and chaque sound similar so it's easy to mix them up.  Here's how to use them correctly.

How to use chacun/chacune and chaque in French

To express each/every in French, there are different expressions depending on sentences:

chaque [chose] each [thing]

To say each/every [thing], you use chaque + [singular noun].

Chaque pays avait envoyé une délégation.Each country had sent a delegation.

Chaque jour, cela devient plus facile.Each day, it becomes easier.

chacun/chacune des [choses] : each of [things]

To say each/every one of [things], you use chacun/chacune des + [plural noun].

Chacune des femmes apporte un plat.Each of the women is bringing a dish.

Chacun des lutins a une tâche spécifique.Each one of the elves has a specific task. 

Chacune des tables était décorée avec goût.Each one of the tables was decorated tastefully. 

ATTENTION

To say each one of us/you/them, you use chacun/chacune d'entre nous/vous/eux/elles (stress pronouns)

Chacun d'entre vous mérite une récompense.Each one of you deserves a reward.

Je respecte chacune d'entre elles.I respect each one of them.
I respect every one of them.

chacun/chacune on their own = each one, every one

To say each/every [one], you use chacun / chacune.

Les filles sont élégantes: chacune porte une robe.The girls are elegant: each one wears a dress.

On a le droit à un gâteau chacun.We're allowed one cake each.

Chacun applies to nouns and was originally the contraction of "chaque+un / chaque+une".
It therefore agrees in gender with the person/group/thing it refers to.

ATTENTION 

You cannot write chaque un as two words.

See also the opposite:
Ne ... aucun(e) = None (French Negations)
and Aucun/e … ne = None (French Negations)

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Examples and resources

Les filles sont élégantes: chacune porte une robe.The girls are elegant: each one wears a dress.
Chaque jour, cela devient plus facile.Each day, it becomes easier.
Chacune des femmes apporte un plat.Each of the women is bringing a dish.
Chaque pays avait envoyé une délégation.Each country had sent a delegation.
Chacun des lutins a une tâche spécifique.Each one of the elves has a specific task. 
On a le droit à un gâteau chacun.We're allowed one cake each.
Je respecte chacune d'entre elles.I respect each one of them.
I respect every one of them.
Chacun d'entre vous mérite une récompense.Each one of you deserves a reward.
Mais dans chaque maison,  Il flotte un air de fête, But in each house,  There's a festive air,    
Chacune des tables était décorée avec goût.Each one of the tables was decorated tastefully. 
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