Question

Use Euclid’s division algorithm to find the HCF of : [5]

(i) 135 and 225 ii. 867 aand 255​

Answer 1

Answer:

By Euclid's Division Algorithm

HCF of 135 and 225

225 = 135 × 1 + 90

135 = 90 × 1 + 45

90 = 45 × 2 + 0

HCF of 135 and 225 = 45

HCF of 867 and 255

867 = 255 × 3 + 102

255 = 102 × 2 + 51

102 = 51 × 2 + 0

HCF of 867 and 255 = 51

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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=45

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.