Real numbers -Euclid’s division algorithm

So, let us state Euclid’s division algorithm clearly.
To obtain the HCF of two integers, say c and d, with c > d , follow the steps below :
Step 1 : Apply Euclid’s division lemma, to c and d. So, we find whole numbers , q and r such that c = dq + r, 0 rStep 2 : If r = 0, d is the HCF of c and d. If r 0, apply the division lemma to d and r.
Step 3 : Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.

This algorithm works because HCF (c,d) = HCF (d,r) where the symbol HCF (c,d) denotes the HCF of c and d, etc.