question_answer

  Using Euclid's division algorithm, find the HCF of 56, 96 and 404.

Answer:

  Given integers are 56, 96 and 404. First we find the HCF of 56 and 96. Applying Euclid's division algorithm, we get Since, the remainder so we apply the division lemma to 56 and 40. Since, the remainder  so we apply the division lemma to 40 and 16. Since,  so we apply the divison lemma to 16 and 8. (2) Clearly, HCF of 56 and 96 is 8. Let us find the HCF of 8 and the third number 404. Applying Euclid's division, we get Since, the remainder is  So, we apply the divison lemma to 8 and 4. We observe that the remainder at this stage is zero. Therefore, the divisor of this stage, i.e., 4 is the HCF of 56, 96 and 404.                      (2)