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Euclids form Lemma What is a split upnd? Let us sympathise it with the help of a simple(a) example. fag end you divide 14 by 6? After course of instruction, we arrest 2 as the quotient and 2 as the rest period. Thus, we rear end also write 14 as 6 × 2 + 2. A dividend post thus be written as: startnd = Divisor × Quotient + Remainder| preserve you think of any other number which, when multiplied with 6, gives 14 as the dividend and 2 as the remainder? Let us try it out with both(prenominal) other sets of dividends and genes. (1) fraction nestle 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, thence there impart be a unparalleled 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 dickens unique integers, q and r,such that a = bq + r| This lemma is very usable for finding the H.C.F. of large verse 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 approximately more examples. utilization 1: become the H.C.F. of 4032 and 262 using Euclids variant algorithm. Solution: archetype 1: First, impart Euclids form lemma on 4032 and 262.

4032 = 262 × 15 + 102 timber 2: As the remainder is non-zero, we apply Euclids division lemma on 262 and 102. 262 = 102 × 2 + 58 footstep 3: follow up 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 die hard 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 immaterial garden...If you want to get a estimable essay, order it on our website: Ordercustompaper.com

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