Traditionally (at least in Spain) garlic was kept in a braided string, hung in a dry place, so that they could last until the following season.
Separating them in cloves will cause them to dry prematurely.
cooking.stackexchange.com/users/52874/roetnig
Most advice I see is to keep the head whole, keep it in the dark, and avoid moisture.
This will allow you to keep garlic for several months.
In my kitchen, I go through several heads of garlic over the course of just one month, so long term storage is not really that critical for me.
I suspect, technically, you would shorten the life span a bit.
Whether or not that matters depends entirely on how quickly you work your way through your garlic stash.
I would say you have little to lose.
Break them apart
(keep the skin on the individual cloves intact), and try it for a few weeks (though, this seems like extra work to me).
If it turns out you use them too slowly, purchase less garlic and keep it whole.
Alternately, store the rest of your whole garlic in a dark, cool, cabinet.
cooking.stackexchange.com/users/17143/moscafj
You can separate them and cut off the end and freeze them.
We do this all the time.
I use a garlic press to use them when needed even while it's frozen.
They seem to last forever.
cooking.stackexchange.com/users/78529/Cece
Breaking them apart to put in a jar - I see several issues.
You will almost certainly break through the skin on a good percentage of them as you separate them into individual cloves, meaning they will have lost their protective layer.
Unless the jar has some kind of desiccant, there is potential for the garlic to sweat & go off rapidly.
The air inside the jar, if anywhere near a source of sunlight, will also be warner than its surroundings, accelerating this still further.
They will all be touching, meaning if one goes bad, the rest will follow in short order.
There is often good, tried & tested sense in traditional storage methods.
The Spanish tradition of weaving them into plaits* is more than decorative - not only does it allow air to circulate to keep the bulbs dry, it also keeps them physically separated in case
one goes bad - it's not going to directly contaminate its neighbours.
*My British father used to do exactly the same with brown onions, so they would last until next year hanging in an outhouse.
I doubt he ever saw a garlic bulb in his life.
cooking.stackexchange.com/users/42066/Tetsujin
It should be fine if you keep the individual clove skins on, the way I see it the outer skin doesn't really add that much extra protection compared to just the inner skin as long as it is not for very long periods.
The bigger risk would be drying out, and it will dry out faster, but the inner skin should suffice as protection almost as effectively as the whole head, so for short periods it should not be very significant.
In my kitchen we even peal individual cloves ahead of time and keep them ready for use in a small jar in the refrigerator.
These keep well for a few weeks at a time.
There may be slight loss of taste over long periods, but I have never seen any go bad.
cooking.stackexchange.com/users/59106/Duarte Farrajota Ramos
An unglazed ceramic vessel should help to regulate the moisture issues that many of the others have mentioned (which would be true in a glass jar).
Glass jars are also problematic as they act as small greenhouses, with the light warming the jar which can cause it to spoil faster.
I would recommend that you fit what garlic you can into the container as whole bulbs/heads, then add your remaining garlic broken up into smaller bits (unpeeled cloves or clumps of cloves).
As you use the garlic, use the fragments first, then break into the whole bulbs.
But the more important thing is to only buy as much garlic as you're going to use in a reasonable amount of time.
If you're not using up your garlic within a month or so, you should probably be buying less garlic each time.
The whole/fragmented method should allow you to tell your older garlic from more a more recent shopping trip -- empty the jar, put the new garlic in as whole bulbs, then break the older garlic apart and fill the jar.
cooking.stackexchange.com/users/67/Joe
I bought jar for garlic but it can store only two bulbs with most place being wasted. Can I separate bulb into cloves and store them? Or will it significantly shorten the lifespan of garlic?  EDIT  To clarify - this is jar made out of ceramic with holes in the bottom for ventilation.
Can I separate garlic into cloves for storage?
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<food-preservation><garlic>
cooking.stackexchange.com/questions/102328
cooking.stackexchange.com/users/39268/Maciej Piechotka
You may be able to separate them into cloves with the skin on without losing too much protection, especially for short periods, but it may still cause them to dry out. Keep as many of the heads whole if you can and keep them in a dark, dry place, or you can separate them, cut off the ends and freeze them.   Garlic is best kept whole. Separating the cloves causes them to dry out faster. If you want to separate them, keep the skin on or remove the skin and freeze.
Separating garlic cloves causes them to dry out quickly. It is recommended that garlic bulbs be kept whole. In a jar, keep as many bulbs whole as possible and only separate when necessary. You can separate if you leave the skin on. After removing the skin, they should be frozen