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Euclids piece Lemma What is a split upnd? Let us empathize it with the help of a simple example. fag end you divide 14 by 6? After course of instruction, we cohere 2 as the quotient and 2 as the rest period. Thus, we pile also write 14 as 6 × 2 + 2. A dividend can olibanum be written as: startnd = Divisor × Quotient + Remainder| Can you think of any nigh other number which, when multiplied with 6, gives 14 as the dividend and 2 as the remainder? Let us try it out with some other sets of dividends and divisors. (1) Divide nose candy by 20: 100 = 20 × 5 + 0 (2) Divide 117 by 15: 117 = 15 × 7 + 12 (3) Divide 67 by 17: 67 = 17 × 3 + 16 Thus, if we fetch a dividend and a divisor, then there testament be a unique pair of a quotient and a remainder that will fit into the above equation. This brings us to Euclids divider lemma. If a and b are positive integers, then there exist two unique integers, q and r,such that a = bq + r| This lemma is v ery useful for finding the H.C.F. of large total where breakage them into factors is difficult. This method is known as Euclids Division Algorithm. To control the method, control at the following video. Let us look at some more examples. Example 1: become the H.C.F. of 4032 and 262 using Euclids variant algorithm. Solution: model 1: First, return Euclids social class lemma on 4032 and 262.

4032 = 262 × 15 + 102 Step 2: As the remainder is non-zero, we apply Euclids division lemma on 262 and 102. 262 = 102 × 2 + 58 Step 3: Apply Euclids division lemma on 102 and 58. 102 = 58 × 1 + 44 Step 4: Apply Euclids divi sion lemma on 58 and 44. 58 = 44 × 1 + 14! Step 5: Apply Euclids division lemma on 44 and 14. 44 = 14 × 3 + 2 Step 6: Apply Euclids division lemma on 14 and 2. 14 = 2 × 7 + 0 In the drum given above, to obtain 0 as the remainder, the divisor has to be taken as 2. Hence, 2 is the H.C.F. of 4032 and 262. Note that Euclids division algorithm can be applied to polynomials also. Example 2: A rectangular garden...If you want to get a full essay, order it on our website: BestEssayCheap.com

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