QUESTION-1

Use Euclid's division algorithm to find the HCF of:

i)135 and 225

ii)196 and 38220

iii)867 and 225

Solution:

i) We start with the larger number i.e 225

By Euclid's division algorithm.we have

225= 1 X 135+90

135=1 x90+45

90=2x45+0

Hence, HCF(225, 135)=HCF(135,90)=HCF(90,45)=45

Therefore.the HCF of 135 and 225 is 45

ii) We start with the larger number i.e 38220

By Euclid's division algorithm.we have

38220= 196 X 195+0

196=196X 1 +0

Hence , HCF(196,38220)=196

Therefore.the HCF of 196 and 38220 is 196

iii) We start with the larger number i.e 867

By Euclid's division algorithm.we have

867=225 X 3+102

225=102 X 2+51

102=51 x2+0

Hence, HCF(867,225)=HCF(225, 102)=HCF(102,51 )=51

Therefore.the HCF of 867 and 225 is 51

Question 2:

Show that any positive odd integer is of the form 6q+1,6q+3 & 6q+5

where q is some integer.

NCERT SOLUTIONS CLASS 10 MATHS

CHAPTER 1 - REAL NUMBERS