1. Use Euclid’s division algorithm to find the HCF of:
(i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255
(i) 135 and 225
To use Euclid’s division algorithm, we apply Euclid’s division lemma to given numbers c and d, to find whole numbers q and r such that
Here,
Remainder is not equal to 0. Therefore, we apply the same process again on 135 and 90
Remainder is not equal to 0 again. Therefore, we apply same process again on 90 and 45.
Remainder is equal to 0.
Therefore, HCF of 135 and 225 is equal to 45 which is equal to value of d in the last step.
(ii) 196 and 38220
To use Euclid’s division algorithm, we apply Euclid’s division lemma to given numbers c and d, to find whole numbers q and r such that
Here,
Remainder is equal to 0.
Therefore, HCF of 196 and 38220 is equal to 196 which is equal to value of d in the last step.
(iii) 867 and 255
To use Euclid’s division algorithm, we apply Euclid’s division lemma to given numbers c and d, to find whole numbers q and r such that
Here,
Remainder is not equal to 0. Therefore, we apply the same process again on 255 and 102
Remainder is not equal to 0 again. Therefore, we apply same process again on 102 and 51.
Remainder is equal to 0.
Therefore, HCF of 867 and 255 is equal to 51 which is equal to value of d in the last step.
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