Question

REAL NUMBERS do EXERCISE 1.1 1. Use Euclid's division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 2. Show that any positive add inteqorin (iii) 867 and 255 ​

Answer 1

Answer:

(i) 45.

Explanation:-

(i) 135 and 225

Sol:- 135<225

Using Euclid's division algorithm-

a=bq+r. { where a and b are integers. And a>b. (q=quotient and r=remainder of a and b)}

step 1- 225=135x1+90

step 2- 135=90x1+45

step 3- 90=45x2+0

so, H.C.F. = 45.

Answer 2

Answer:

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Step-by-step explanation:

By Euclid's division lemma,

225=135×1+90

r=90

135=90×1+45

r=4

90=45×2+0

So,  H.C.F of 135 and 225 is 45

(ii) By Euclid's division lemma,

38220=196×195+0r=0

So, H.C.F of 38220 and 196 is 196

(iii) By Euclid's division lemma,

867=255×3+102

r=10

255=102×2+51

r=51

102=51×2+0

So, H.C.F of 867 and 255 is 51

The highest HCF among the three is 196.