Question

REAL NUMER
EXERCISE 1.1
KUse Euclid's division algorithm to find the HCF of:
(1) 135 and 225
(u) 196 and 38220
2. Show that any positive odd integer is of the form 6q+1. or
su integer​

Answer 1

Answer:

since 225 greater than 135

we divided 225 by 135

225 ÷135 =1

remainder =90

since reminded is not zero

we divided 135 by 90

135÷ 90=1

reminder 45

again, since reminder is not zero

45÷ 90=2

since remainder is now zero

c f of 135 and 225 is 45

Answer 2

Step-by-step explanation:

(i) 135 and 225

sol- 225>135

by Euclid division algorithm

225 = 135 × 1 + 90

again by Euclid division algorithm

135 = 90 × 1 + 45

again by Euclid division algorithm

90 = 45 × 2 + 0

HCF(135,225)=45

(ii)196 and 38220

sol- 38220>196

by Euclid division algorithm

38220=196×195+0

HCF of (38220,196)=196

2 sol- let a be any positive odd integer

by Euclid division algorithm

a = 6q+0 ___(i)

a = 6q+1 ___(ii)

a = 6q+2 ___(iii)

a = 6q+3 ___(iv)

a = 6q+4 ___(v)

a = 6q+5 ___(iv)

hence, a is odd , IN EQUATION (i) , (iii) ,(v) is not possible.

Therefore, any odd number is in the form (ii) ,(iv) ,and (vi).

thankyou, hope it works for all