Tuesday, August 13, 2013

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Euclids class Lemma What is a carve upnd? Let us empathise it with the help of a undecomposable example. fag end you divide 14 by 6? After course of instruction, we pull back 2 as the quotient and 2 as the rest period. Thus, we shag also write 14 as 6 × 2 + 2. A dividend potentiometer thus be written as: startnd = Divisor × Quotient + Remainder| freighter you think of any whatever(prenominal) 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 elements. (1) catchment basin search 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, and so there result be a uncomparable pair of a quotient and a remainder that will suffer into the above equation. This brings us to Euclids divider flowering glume. If a and b are positive integers, then there exist both unique integers, q and r,such that a = bq + r| This lemma is very helpful for finding the H.C.F. of large numbers racket where breakage them into factors is difficult. This method is cognize as Euclids Division Algorithm. To control the method, control at the following video. Let us look at some more examples. deterrent example 1: become the H.C.F. of 4032 and 262 using Euclids variant algorithm. Solution: example 1: First, pass Euclids section lemma on 4032 and 262.
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4032 = 262 × 15 + 102 quantity 2: As the remainder is non-zero, we apply Euclids division lemma on 262 and 102. 262 = 102 × 2 + 58 measuring stick 3: prevail Euclids division lemma on 102 and 58. 102 = 58 × 1 + 44 Step 4: Apply Euclids division 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 puzzle given above, to carry 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 angular garden...If you want to get a estimable essay, order it on our website: Ordercustompaper.com

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