Question

Activity to find the h.c.f. of two numbers experimentally based on euclid's division lemma or algorithm.

Answer 1

Activity to find the h.c.f. of two numbers experimentally based on euclid's division lemma or algorithm-----
Euclid’s division lemma: IT states that for any given two positive integers ‘a’ and ‘b’ we can find two whole numbers ‘q’ and ‘r’ such that a = b × q + r  where 0 ≤ r < b.
It is used to find the highest common factor of any given two positive integers and also to depict the common properties of numbers.
The following steps to obtain H.C.F using Euclid’s division lemma: 1. Consider two positive integers ‘a’ and ‘b’ such that a > b.2. Apply Euclid’s division lemma to the given integers ‘a’ and ‘b’ to find two whole numbers ‘q’ and ‘r’ such that, a = b x q + r.3. Check the value of ‘r’. If r = 0 then ‘b’ is the HCF of the given numbers. 4. If r ≠ 0, apply Euclid’s division lemma to find the new divisor ‘b’ and remainder ‘r’.5. Continue this process till the remainder  becomes zero. In that case the value of the divisor ‘b’ is the HCF (a , b). Also HCF(a ,b) = HCF(b, r).