Class 10th Maths Real no/Part 2 By Mugdha Pandit

1. Xkf.kr
d{kk 10 oh
Chapter -1
okLrfod la[;k,a
Real Numbers

2. okLrfod la[;k,a
Real Numbers

3. ge i<saxs&
vad xf.kr dh vk/kkjHkwr izes;
iwoZ Kku%& ge tkurs gSa----
fdlh Hkh izkd`r la[;k dks vHkkT; xq.ku[k.M ds :Ik esa fy[kk
tk ldrk gSA
 tSls ---------2= 2
 4= 2X2 6= 2X3 vkfn
vHkkT; la[;k 2]3]5]7]11]13]17]19]23--------- esa ls dqN ;k lHkh
la[;kvksa dk ge xq.kk djsa rks /kukRed iw.kkZadksa dk laxzg cuk ldrs gsaaA
tSls--------- 2X3X5= 30
3X5X7= 105
3X7X11X23= 5313

4. ‘;fn ge vHkkT; la[;kvksa dks lHkh laHko izdkjksa ls la;ksftr djsa rks
gesa lHkh vHkkT; la[;kvksa vkSj vHkkT; la[;kvksa ds lHkh laHko
xq.kuQyksa dk ,d vuar laxzg izkIr gksxkA
D;k ge bl izdkj lHkh HkkT; la[;k,a izkIr dj ldrs gSa vkb;s ns[ksa
&
,d cMh la[;k ysa vkSj mldk xq.ku[k.M djsa &

5. 32760
16380
8190
4095
1365
455
91
13
2
2
2
3
3
5
7
,d cMh la[;k ysa vkSj mldk xq.ku[k.M
djsa&
32760=2X2X2X3X3X5X7X13

6. xq.ku[k.M djus ij &
32760=2X2X2X3X3X5X7X13
vFkkZr 32760=23X32X5X7X13
tks vHkkT; la[;kvksa dh ?kkrksa ds :i esa gSaA
vr% ge dg ldrs gSa fd izR;sd HkkT; la[;k dks vHkkT; la[;kvksa
dh ?kkrksa ds xq.kuQy ds :i esa fy[kk tk ldrk gS vkSj ;g
xq.ku[kaMu vHkkT; xq.ku[kaMksa ds vkus okys dze ds fcuk vf}rh;
gksrk gSA
;gh vadxf.kr dh vk/kkjHkwr izes; gSA

7. vad xf.kr dh vk/kkjHkwr izes; ds vuqiz;ksx
vHkkT; xq.ku[k.M fof/k
vad xf.kr dh vk/kkjHkwr izes; dk iz;ksx dj nks /kukRed iw.kkZadksa
ds HCF o LCM Kkr djus dh fof/k dks vHkkT; xq.ku[k.M
fof/k dgrs gSaA
• HCF ¼egRre lekiorZd½= la[;kvksa esa izR;sd mHk;fu"B¼nksuks esa
lekku½ vHkkT; xq.ku[k.M dh lcls NksVh ?kkr dk xq.kuQy
• LCM ¼y?kqRre lekiorZd½= la[;kvksa esa lac) izR;sd vHkkT;
xq.ku[k.M dh lcls cMh ?kkr dk xq.kuQy
fdUgha nks /kukRed iw.kkZadksa a vkSj b ds fy,
HCF(a,b) X LCM(a,b) = aXb

8. mnkgj.k%&140 dks vHkkT; xq.kuQy ds :Ik esa O;Dr
dhft,A
gy%& 140
2)140
2)70
5)35
7) 7
1 140=2X2X5X7
vFkkZr 140=22X5X7

9. mnkgj.k%&la[;k 6 ,oa 20 dk vHkkT; xq.ku[k.M fof/k ls
HCF o LCM Kkr djuk
gy%&
2)6 2)20
3)3 2)10
1 5)5
1
6=2X3X5 6=21X31X51
20=2X2X5 20=22X51
HCF= 2 ¼nksuks la[;kvksa esa izR;sd mHk;fu"B vHkkT; xq.ku[k.M dh lcls NksVh ?kkr dk xq.kuQy ½
LCM=2X2X3X5=60 ¼nksuks la[;kvksa esa lac) izR;sd vHkkT; xq.ku[k.M dh lcls cMh ?kkr dk
xq.kuQy½
mRrj dh tkWap& HCF(a,b) X LCM(a,b) = aXb
2 X 60 = 6 X 20
120 = 120

10. mnkgj.k%&la[;k 12]15 ,oa 21 dk vHkkT; xq.ku[k.M fof/k ls HCF o
LCM Kkr djuk
gy%&
2)12 3)15 3)21
2)6 5)5 7)7
3)3 1 1
1
12=2X2X3 12=22X31
15=3X5 15=31X51
21=3X7 21=31X71
HCF= 3 ¼rhuks la[;kvksa esa izR;sd mHk;fu"B vHkkT; xq.ku[k.M dh lcls NksVh ?kkr dk
xq.kuQy ½
LCM=2X2X3X5X7=420 ¼nksuks la[;kvksa esa lac) izR;sd vHkkT; xq.ku[k.M dh lcls
cMh ?kkr dk xq.kuQy½

11. mnkgj.k%&la[;k 26 ,oa 91 dk vHkkT; xq.ku[k.M fof/k ls HCF Kkr
dhft, o fQj budk LCM Kkr dhft,A
gy%&
2)26 7)91
13)13 13)13
1
26=2X13 26=21X131
91=7X13 91=71X131
HCF= 13 ¼nksuks la[;kvksa esa izR;sd mHk;fu"B vHkkT; xq.ku[k.M dh lcls NksVh ?kkr dk xq.kuQy
½
HCF(a,b) X LCM(a,b) = aXb
LCM(a,b)= aXb/ HCF(a,b)
= 26 X 91 / 13
=182
mRrj%& HCF= 13, LCF= 182

12. vH;kl iz’u
1- ;fn a o b nks /kukRed iw.kkZad gks rks HCF(a,b) X LCM(a,b) =
aaaa) aXb b) a─b c) a+b d) a/ b
2- nks la[;kvksa dk HCF=6 vkSj LCM=60 gS] osa la[;k,a gSa&
aaaa) 10 o 36 b) 24 o 15 c) 12 o 30 d) 18 o 20
3- 156 dks vHkkT; xq.kuQy ds :Ik esa O;Dr dhft,A
4- la[;k 510 ,oa 92 dk vHkkT; xq.ku[k.M fof/k ls HCF o LCM Kkr
dhft,A
5- la[;k 6]72 ,oa 120 dk vHkkT; xq.ku[k.M fof/k ls HCF o LCM
Kkr dhft,A
6- la[;k 96 ,oa 404 dk vHkkT; xq.ku[k.M fof/k ls HCF Kkr dhft,
o fQj budk LCM Kkr dhft,A

13. /kU;okn
eqX/kk iafMr
Ákpk;Z
‘ ’kkl- gkbZLdwy C;kojk
mTtSu ¼ e-iz-½