Divisors thiab zauv

"Ntau tus xov tooj" npe kawm nyob rau hauv lub qib 5 ntawm ob lub tsev kawm ntawv. Nws lub hom phiaj yog los txhim kho hais lus thiab sau cov txuj ci ntawm zauv. Zaj lus qhia no qhia lub ntsiab tshiab - lub "zauv" thiab "splitters", yog ua tiav raws li cov txheej txheem ntawm kev nrhiav cov divisors thiab cov zauv ntawm ib tug tej yam ntuj tso tooj, muaj peev xwm nrhiav tau cov NOC nyob rau hauv ntau txoj kev.

Cov npe no yog qho tseem ceeb heev. Paub txog nws yuav tau mus thov nyob rau hauv kev daws piv txwv nrog cov zauv feem. Ua li no, koj yuav tsum nrhiav ib qho denominator los xam xyuas qhov tsawg heev ntau (LCM).

Ib tug quav yog suav tias yog ib qho integer uas yog divisible los ntawm tsis muaj ib txoj lw.

18: 2 = 9

Txhua zoo integer muaj infinitely ntau zauv xov tooj. Nws yog nws tus kheej xav tau tsawg tshaj plaws. Quav tsis tau muaj tsawg tshaj li tus xov tooj rau nws tus kheej.

ua hauj lwm

Peb muaj los ua pov thawj hais tias cov xov tooj 125 yog ib tug ntau yam ntawm tus xov tooj 5. Ua li no, faib cov thawj xov tooj rau lub thib ob. Yog hais tias lub 125 yog divisible los ntawm 5 yam tsis muaj ib tug kab, ces cov lus teb no yog.

Tag nrho tej yam ntuj tso tus xov tooj yuav tsum tau muab faib mus rau hauv: 1. Ntau divides rau nws tus kheej.

Raws li peb paub, cov xov tooj ntawm fission yog hu ua "tawn", "divider", "private".

27: 9 = 3,

qhov twg 27 - tawn, 9 - divider 3 - quotient.

Cov zauv ntawm 2, - cov neeg uas thaum muab faib ua ob tsis tsim ib tug residue. Lawv yog cov tag nrho cov txawm.

Cov zauv ntawm 3 - yog zoo li no hais tias tsis muaj residues raug muab faib ua peb (3, 6, 9, 12, 15 ...).

Piv txwv li, 72. Qhov no tus xov tooj yog ib tug ntau yam ntawm 3, vim hais tias nws yog divisible los ntawm 3 tsis muaj seem (raws li yog lub npe hu, tus xov tooj yog divisible los ntawm 3 tsis muaj tas, yog hais tias tus sum ntawm nws tug lej tom qab yog divisible los ntawm 3)

lub sum ntawm 7 + 2 = 9; 9: 3 = 3.

Yog tus xov tooj 11, ib tug ntau yam ntawm 4?

11: 4 = 2 (residue 3)

Teb: tsis yog, raws li muaj ib tug tshuav nyiaj li cas.

Common ntau ntawm ob los yog ntau tshaj cov zauv - nws yog, uas yog muab faib los ntawm tus xov tooj ntawm tsis muaj residue.

K (8) = 8, 16, 24 ...

K (6) = 6, 12, 18, 24 ...

K (6.8) = 24

LCM (tsawg kawg yog ntau ntau yam) yog raws li nram no.

Rau txhua tooj tsim nyog los ib lub zuj zus sau rau hauv cov hlua zauv - kom txog rau thaum nrhiav tau tib yam.

NOC (5, 6) = 30.

Qhov no txoj kev muaj feem xyuam rau me.

Thaum xam NOC raws li tshwj xeeb no.

1. Yog hais tias koj yuav tsum nrhiav ib qho ntau ntawm 2 tus xov tooj (xws li, 80 thiab 20), qhov chaw uas ib tug ntawm lawv (80) yog divisible los ntawm lwm (20), ces qhov no tus xov tooj (80) thiab yog qhov tsawg tshaj plaws ntau yam ntawm cov ob tug zauv.

NOC (80, 20) = 80.

2. Yog hais tias ob prime xov tooj tsis muaj ntau divisor, peb yuav hais tias lawv NOC - yog qhov khoom ntawm cov ob tug zauv.

NOC (6, 7) = 42.

Xav txog qhov kawg piv txwv. 6 thiab 7 nrog rau kev hwm rau 42 yog divisors. Lawv muab ib tug ntau yam uas tsis muaj residue.

42: 7 = 6

42: 6 = 7

Nyob rau hauv qhov kev piv txwv, 6 thiab 7 yog paired divisors. Lawv cov khoom no yog sib npaug zos rau ib tug ntau yam ntawm (42).

6x7 = 42

Tus xov tooj no yog hu ua prime yog hais tias tus los yog 1 (3: 1 = 3 3 3 = 1) yog divisible nkaus xwb los ntawm nws tus kheej. Lwm tus yog hu ua puas.

Nyob rau hauv lwm cov piv txwv, qhov yuav tsum tau los mus txiav txim seb tus divider 9 nrog rau kev hwm mus 42.

42: 9 = 4 (residue 6)

Teb: 9 tsis yog ib tug divisor ntawm 42 vim hais tias muaj yog ib tug tshuav nyiaj li cas nyob rau hauv lub teb.

Lub divider yog txawv los ntawm lub sij hawm uas lub divider - qhov no yog lub xov tooj los ntawm cov uas faib lub ntuj tus xov tooj, thiab quav nws tus kheej yog muab faib los ntawm tus xov tooj.

Qhov loj tshaj ntau divisor ntawm cov zauv ib tug thiab b, multiplied los ntawm lawv cov tsawg tshaj plaws quav, muab lawv tus kheej cov khoom ntawm cov zauv ib tug thiab b.

Namely: GCD (a, b) x LCM (a, b) = ib tug x b.

Common cov zauv ntawm ntau cov xov tooj raws li nram no.

Piv txwv li, mus nrhiav tau cov NOC rau 168, 180, 3024.

Cov lej no tej yog decomposed rau hauv prime yam, sau raws li cov khoom ntawm powers:

168 = 2³h3¹h7¹

= 180 2²h3²h5¹

3024 = 2⁴h3³h7¹

Ces sau tag nrho cov puag degrees nrog rau cov loj tshaj kev kawm thiab muab lawv:

2⁴h3³h5¹h7¹ = 15120

NOC (168, 180, 3024) = 15120.