Question -
Answer -
i. 135 and 225
ii. 196 and 38220
iii. 867 and 225
Solutions:
Q i. 135 and 225
i. 135 and 225
As you can see, from the question 225 isgreater than 135. Therefore, by Euclid’s division algorithm, we have,
225 = 135 × 1 + 90
Now, remainder 90 ≠ 0, thus again usingdivision lemma for 90, we get,
135 = 90 × 1 + 45
Again, 45 ≠ 0, repeating the above step for45, we get,
90 = 45 × 2 + 0
The remainder is now zero, so our method stopshere. Since, in the last step, the divisor is 45, therefore, HCF (225,135) =HCF (135, 90) = HCF (90, 45) = 45.
Hence, the HCF of 225 and 135 is 45.
Q ii. 196 and 38220
ii. 196 and 38220
In this given question, 38220>196,therefore the by applying Euclid’s division algorithm and taking 38220 asdivisor, we get,
38220 = 196 × 195 + 0
We have already got the remainder as 0 here.Therefore, HCF(196, 38220) = 196.
Hence, the HCF of 196 and 38220 is 196.
Q iii. 867 and 225
iii. 867 and 225
As we know, 867 is greater than 225. Let usapply now Euclid’s division algorithm on 867, to get,
867 = 225 × 3 + 102
Remainder 102 ≠ 0, therefore taking 225 asdivisor and applying the division lemma method, we get,
225 = 102 × 2 + 51
Again, 51 ≠ 0. Now 102 is the new divisor, sorepeating the same step we get,
102 = 51 × 2 + 0
The remainder is now zero, so our procedurestops here. Since, in the last step, the divisor is 51, therefore, HCF(867,225) = HCF(225,102) = HCF(102,51) = 51.
Hence, the HCF of 867 and 225 is 51.