cardinal numbers without nouns (maoluimhreacha):

• are used as nouns.
• they (1-19) are always used with the numeral particle a (a haon, a dó, a trí, etc.)
• the even tens (except deich = 10) are mostly seen without a particle (fiche = 20, tríocha = 30, caoga = 50). This is because the even tens (except deich = 10) count as real nouns
• The numeral particle does then appear when a ten is combined with the numbers 1-19 (fiche a hocht = 28, caoga a naoi = 59, fiche a trí déag = 33).
• they are used when counting (a haon, a dó, a trí, a ceathair, ... = 1, 2, 3, 4, ...) and numbering (bus a haon = Bus Nr. 1)
  and in arithmetic (a haon agus a dó sin a trí = 1 + 2 is 3)
• This form is the same as the adjectival cardinal numbers with a noun, except in the case of 2, 4 (and also 12, 14 etc.):
  comp. a dó - dhá, a ceathair - ceithre)
• The numbers 11-19 are formed using an affixed déag (-ten): a haon déag = 11
• déag is lenited after dó, but not after the other numbers (a dó dhéag = 12 but: a trí déag = 13)
  a haon déag is pulled together when spoken (nd > nn), as if a haonnéag was written there [@ hi:Ne:g, @ he:ne:g]
• Instead of fiche a haon also a haon is fiche etc.
• The numeral particle is not used in selections : bád nó dhó = one boat or two; trí nó ceathair de bháid = three or four boats
• for the numbers from 20-99 there are 2 ways of counting: the decimal system (in base ten) and the vigesimal system (in base twenty), see overview numbers from 20-99
  decimal: seachtó a dó = 72
  vigesimal: trí fichid a dó dhéag = 72 (lit.: "3x20 + 12")
• Null is náid, often without a numeral particle.
• A use with other nouns may only follow with the aid of the preposition de: e.g.: a trí déag de chapaill = 13 of the horses. Otherwise one uses the adjectival forms given below

cardinal numbers with nouns (uimhreacha néamhphearsanta):

• they are used like adjectives but come before the noun, as opposed to other adjectives.
• they are used in specifying a quantity of things (trí bhád = 3 boats)
• The number 1: There are 3 possibilities for "one boat":
  bád = bád amháin = aon bhád amháin = one boat
  but not : aon bhád: this takes the meaning of "any boat," in questions, or in negativen sentences, "no boat":
  An bhfuil aon bhád agat? = Do you have a boat?, Níl aon charr agam = I don't have a car
• The numbers 2-10 und 12 are sometimes used with quantities of people (except duine), but mostly in their place on uses the special numbers of person: trí fhear = tríúr fear = 3 men
• The noun following 1 is always in the singular and is (after aon) lenited
  e.g. aon bhád amháin = 1 boat
• The noun following 2 (dhá) is always in the singular and is lenited, if possible (2nd declension) in the dual-form* (the dual is equivalent to the dative form)
  e.g.: dhá bhád = 2 boats (singular), dhá mhuic = 2 pigs (muic is the dial of muc), dhá láimh = 2 hands (láimh is the dual of lámh)
• The noun following 3-10 is today mostly in the singular, but it is
  • lenited after 3-6 (e.g.: trí bhád = three boats)
  • eclipsed after 7-10 (e.g.: seacht mbád = seven boats)
• less commonly, the noun following 3-10 is in the plural, but it is
  • not lenited after 3-6 (e.g.: trí bliana = three years )
    (an h-prefix preceding a vowel: e.g.: trí huibhe = 3 eggs )
  • eclipsed after 7-10 (e.g.: seacht mbliana = seven years )
  The plural after 3-10 ist always used when:
  • counting of years (special plural form for bliain: bliana):
    aon bhliain, dó bhliain, trí bliana, sé bliana, seacht mbliana, etc.
  • The gen. noun ceann (= "piece" lit. "head"), plural: cinn
    ceann = 1 piece, dhá cheann = 2 pieces, trí cinn = 3 pieces, seacht gcinn = 7 pieces
    (instead of ceann there are also similar words in this vein)
  • units of measurement and the like: e.g.: trí cinn = 3 pieces, trí huaire = 3 hours, three times, trí huibhe = 3 eggs, trí fichid/trí scóir = 3 x 20, trí scilinge = 3 shillings, trí pingine = 3 pence
• With the numbers from 11-19 déag comes after the noun: trí bhád déag = 13 boats
  otherwise they acta as the numbers from 1-10
  déag (-ten) is lenited after a noun with a final vowel sound (in the singular), e.g.: aon chóta dhéag = 11 coats . This isn't the case if the noun is in the plural: trí bliana déag = 13 years
• after even steps of tens or twenties (except deich) nouns are unlenited and always in the singular (originally, this is the genitive plural), e.g.: tríocha bád = 30 boats, caoga ceann = 50 pieces, fiche bliain = 20 years

  with a following adjective:

• an adj. after aon + feminine noun is lenited and is in the singular e.g: aon bhean mhór amháin
• an adj. after aon + masculine noun remains unlenited in the singular e.g: aon fhear mór amháin
• an adj. after dhá till deich + noun is lenited and is in the plural e.g: dhá bhád mhóra, seacht mbád mhóra
  (if one uses a noun in the plural after 3-10, lenition of the adjective follows only then if the noun ends in a slender consonant: e.g. trí capaill mhóra = 3 big horses , otherwise not: trí bróga móra = 3 big shoes )

  with an article

• the singular article an precedes 1, 2, 11, 12 (dhá after an article de-lenited to dá).
  e.g.: an t-aon bhád déag = the 11 boats, an dá bhád = the 2 boats, an dá bhád déag = the 12 boats.
  In the genitive, the t-prefix is omitted on aon with a masc. noun : an aon, preceding femin. nouns, though still na haon; an dá remains unchanged. (after aon one also commonly places the noun in the genitive)
  e.g.: seolta an aon bháid déag = the sails of the eleven boats, leabhar na haon mhná amháin = the book of the one woman, seolta an dá bhád = the sails of the two boats.
• plural-article na precedes 3-10 and 13-19:
  e.g.: na trí bhád = the 3 boats, na ceithre bhád = the 4 boats, na hocht mbád = the 8 boats.
  In the genitive there is eclipsis on the number:
  e.g.: seolta na dtrí bhád = the sails of the 3 boats, stábla na gceithre bho = the stall of the 4 cows
• singular article an preceding even tens (except deich):
  e.g.: an fiche bliain = the 20 years, an caoga bád = the 50 boats.
• céad/míle also in the plural (with the plural article: na) na céadtha / na mílte = hundreds/thousands of... After this, follows the noun, mostly in the plural: na céadtha mná = hundreds of women

  miscellaneous and variants

• ceithre, cúig appear often in lenited form (cheithre, chúig)
• preceding dhá always in instead of i (e.g.: in dhá bhaile = in two towns)
• fiche is a noun, which can be declined (5th declension ):
  genitive fichead, dative fichid, plural fichid (with other numbers, otherwise: fichidí)
  similarly, the other powers of 10 are declined
• instead of fiche/fichid also scór/scóir (after that also nouns in the plural are possible.)
• instead of is fiche, is tríocha etc.  of course also agus fiche, agus tríocha
• instead of is fiche ("and 20") then also fichead ("of 20") or ar fhichid ("on 20") are possible and vice versa
    - trí bhád is fiche / agus fiche = 23 boats ("3 boats and 20")
    - trí bhád fichead = 23 boats ("3 boats of 20")
    - trí bhád ar fhichid = 23 boats ("3 boats on 20")
• Instead of e.g. is caoga, is seachtó ("and 50", "and 70") equivalent to caogad, seachtód ("of 50", "of 70") or ar caogaid, ar seachtóid ("on 50", "on 70") etc. are possible (but not as common as with fiche)
    - trí bhád is seachtó = 73 boats ("3 boats and 70")
    - trí bhád seachtód = 73 boats ("3 boats of 70")
    - trí bhád ar seachtóid = 73 boats ("3 boats on 70")
• instead of céad is dhá bhád then dhá bhád is céad/ar chéad (102 boats); despite the rule of thumb that numbers over one hundred have céad leading.
• The twenties or vigesimal system can also be used above 100 : e.g.: sé fichid bád = 120 boats (lit.: "6x20 boats") instead of: céad is fiche bád = 120 boats;
  seacht bhfichid = 140 ("7x20"), cúig fichid = 100, ocht bhfichid = 160, naoi bhfichid = 180, etc.
• instead of dhá cheann then péire = both
• instead of 12 then doiséinne or dosaen ( = dozen):
  e.g.: doiséinne uibheacha = a dozen eggs , in multiples: dhá dhosean uibheacha = two dozen eggs, deich ndosaen uibheacha = 120 eggs .
• daichead (40) is the compact form of dá fhichead ("2x20"),
  instead of that one, also dhá scór (+ noun in the plural) or ceathracha (analog to tríocha = 30)
• instead of caoga or dhá fhichead a deich (50) also leathchéad ("half a hundred")
  e.g.: caoga bád = deich mbád is dá fhichead = leathchéad bád = 50 boats
  equivalent to céad go leith = 150 (lit.: "100 with half ")
• punt (pound) vor déag (also 11-19) always punta
  e.g.: dhá phunta dhéag = 12 pounds

numbers of person (uimhreacha pearsanta):

• numbers of person are used to count people.
• they are nouns (as opposed to the adjectival cardinal numbers).
• there are only ones for from 2-10, as well as a special form for 12
• 3-10 are masculine and originally contractions of normal cardinal number and fear = man: trí fhear > tríúr. They are used for women as well (tríúr ban = 3 women ), 2 (beirt) is a feminine noun
• for the numbers 1, 11 and above 13 there are no special numbers of person, i.e. one uses the normal cardinal numbers
• they may occur on their own or in connection with nouns that describe persons:
  e.g.: tríúr = 3 people, tríúr fear = 3 men, tríúr ban = 3 women, tríúr múinteoir = 3 teachers
  Nouns denoting peopls can also be used with adjectival cardinal numbers, but this is less common (tríúr ban = 3 women , less common would be trí bhean)
  the noun duine = person is already included in the noun of person: 3 people = tríúr not *tríúr duine
• a following noun is unlenited after 3-10, but is lenited after beirt,
  • in the genitive plural (older standard variant) e.g. beirt fhear, tríúr ban, ochtar banaltraí
  • in the nominative-singular (but bean is always in the gen. plural: ban) e.g. ochtar banaltra
    a following adjective would then be in the nominative singular, after beirt, in the plural e.g. beirt fhear mhóra, tríúr fear mór
  • in the dative plural, with the preposition de: triúr d'fhir, ochtar de mhná
• expressions like "as a threesome ", "as a foursome ", etc. are formed with the preposition i and the possessive pronoun: Bhí siad ina n-ochtar ann = they were there as a group of eight. (lit.: "were they in-their eight[-man] there "); Rinne muid inár gcúigear é = we did it as a group of five.
• without a following noun, numbers of person can also be used as a substitute for number + ceann when counting inanimate objects: trí cinn = triúr = 3 pieces
  e.g. "Cé mhéad leabhar?" - "Tríúr" (eng.:"How many books ?" - "3 (pieces)")
• with the article: dháréag is delenited to dáréag after the article: an dáréag aspal = the 12 Apostles
  ochtar with article always takes the t-prefix: an t-ochtar, but not in the genitive and dative: ar an ochtar = on the 8 people
• instead of beirt = two also dís is possible, instead of seachtar = seven also mórsheisear (lit. "big six ")
• The word aonar is due to its origin a number of person ("one person "), but is hardly used in that sense (instead of that is means "alone" Tá mé i m'aonar = I am alone (lit.: "I am in my one person "). It is used as the other expressions like "threesome" , so it quasi literally means "onesome"

ordinal numbers (orduimhreacha):

• ordinal numbers appear mostly with the article.
• after chéad (= 1st ) lenition occurs: an chéad fhear = the first man
• after dara (= 2nd ) upwards, no lenition: an triú fear = the third man, but h-prefix precedes a vowel: an tríú hulla = the 3rd apple, an dara háit = the 2nd place
• The suffix -ú in older orthography was written -mhadh: seachtmhadh = seachtú = 7.
• after the ordinal number, the noun is always in the nominative, almost never in the genitive: clann an dara bean = the children of the 2nd wife
• after the ordinal number and the noun there is usually no genitive attribute: an dara bean chéile le Seán = Seán's 2nd wife
• with the ordinal number and the noun there is mostly no possessive pronoun needed: an dara bean chéile aige = his 2nd wife
• Instead of dara then darna (= 2nd ), instead of tríú then treas (= 3rd )
• Instead of dóú ....déag then dara....déag (= 12th)
• The abbreviated form with numerals (like: 1st , 2nd , 3rd ) is done in Irish with a ú (1ú, 2ú, 3ú), with 1st and 2nd one can also find 1d, 2a.
  Is é Lá Fheile Pádraig an 17ú lá den Márta = Saint Patrick's Day is the 17th of March.
  When the date is stated, this is mostly done so with further simplification: an 17ú lá den Márta 2003 = 17 Márta 2003

Footnote:
*: The dual stood earlier in Indoeuropean languages next to the singular and the plural
The remnants in Irish (as a composite of singular/plural) are:

1. the singular article (an) preceding two  e.g.: an dá bhád = the two boats (instead of the otherwise necessary plural article na preceding 3-10: na trí bhád = the three boats)
2. if it exists, a noun after two is in the dual form (= dative singular form) e.g. dhá bhróig =two shoes
3. otherwise, the nominative singular form of the noun always comes after two e.g.: dhá bhád = two boats (after 3-10 also the plural is possible)
4. following adjectives are then still in the plural e.g. an dá bhád mhóra = the two big boats (like with 3-10)