CHAPTER 1 REAL NUMBERS
Theorem 1: Euclid’s Division Lemma
Euclid’s division algorithm To obtain the HCF of two positive 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 ≤ r < d. Step 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. Theorem 2: Fundamental Theorem of Arithmetic
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Theorem 6:
Theorem 7:
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