CLASS 10 CH:-1 REAL NUMBER

QUESTION 1: USE EUCLIDE'S DIVISION ALGORITHM TO FIND THE HCF OF:

1)135 AND 225       2) 196 AND 38220         3) 867 AND 255

 SOLUTION 1:

1)135 AND 225

    SINCE 225>135, WE APPLY THE DIVISION LEMMA TO 225 AND 135 TO     OBTAIN .

    225=135*1+90

    135=90*1+45

    90=2*45+0

  SINCE THE REMINDER IS ZERO, THE PROCESS STOPS. SINCE THE  DIVISOR    AT THIS STAGE IS 45, THEREFORE, THE HCF OF 135 AND 225 IS 45.

  2) 196 AND 38220

SINCE 38220>196, WE APPLY THE DIVISION LEMMA TO 38220 AND 196 TO OBTAIN 

  38220=196*195+0

 SINCE THE REMAINDER IS ZERO, THE PROCESS STOPS. 

SINCE THE DIVISOR AT THIS STAGE IS 196,

THEREFORE, HCF OF 196 AND 38220 IS 196.

3) 867 AND 255

SINCE 867>255, WE APPLY THE DIVISION LEMMA TO 867 AND 255 TO OBTAIN

867=255*3+102

255=102*2+51

102=51*2+0

SINCE THE REMAINDER IS ZERO, THE PROCESS STOPS. 

SINCE THE DIVISOR AT THIS STAGE IS 51.

THEREFORE, HCF OF 867  AND 255 IS 51.