Mathematics

Mathematics, 28.10.2019 00:43, firenation18

What is the greatest common divisor of 54 36 and 24

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Computers and Technology, 22.06.2019 05:20, ashcormu11

Write a program called assignment3 (saved in a ﬁle assignment3.java) that computes the greatest common divisor of two given integers. one of the oldest numerical algorithms was described by the greek mathematician, euclid, in 300 b.c. it is a simple but very e↵ective algorithm that computes the greatest common divisor of two given integers. for instance, given integers 24 and 18, the greatest common divisor is 6, because 6 is the largest integer that divides evenly into both 24 and 18. we will denote the greatest common divisor of x and y as gcd(x, y). the algorithm is based on the clever idea that the gcd(x, y) = gcd(x ! y, y) if x > = y and gcd(x, y) = gcd(x, y ! x) if x < y. the algorithm consists of a series of steps (loop iterations) where the “larger” integer is replaced by the di↵erence of the larger and smaller integer. this continues until the two values are equal. that is then the gcd.

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Computers and Technology, 31.08.2019 05:10, nanaflower321

Let a = { 0, 1, 2, 3, 4, 5, 6 }, let b = { 0, 1, 2, 3, 4, 5, 6, 7, 8 }, and let r be the relation from a to b given by "the greatest common divisor of a and b is 2." [note: "greatest common divisor" is sometimes called "highest common factor".] list the elements of r.

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Mathematics, 14.09.2019 05:30, letsgivepece2309

Let a (0,1,2,3,4,5,6, let b (0,1,2,3,4,5,6,7,8), and let r be the relation from a to b given by "the greatest common divisor of a and b is 2." [note: "greatest common divisor" is sometimes called "highest common factor"] list the elements of r. t: aph (v,r3 veith pivesn v anel : v p,grs, nll«.sl.lv.sl.lp.sl.lp.s.tp.

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Computers and Technology, 09.10.2019 17:20, erykp17

4[bvg 3.6 (modified)] in this exercise, all integers are considered to be nonnegative, for simplicity. a divisor of an integer k is any integer d 6= 0 such that k/d has no remainder. a common divisor for a set of integers is an integer that is a divisor for each integer in the set. euclid’s algorithm for finding the greatest common divisor (gcd) of two nonnegative integers, m and n, can be written as follows: 1: procedure gcd(int m,int n) 2: if n = 0 then 3: nser ← m 4: else if m < n then 5: nser ← gcd(n, m) 6: else 7: r ← m − n · b m n c . r is the remainder of m n 8: nser ← gcd(n, r) 9: end if 10: return nser 11: end procedure the preconditions for gcd(m, n) are that m ≥ 0, n ≥ 0 and m + n > 0. prove the following using induction. a. if the preconditions of gcd(m, n) are satisfied, then the value that the function returns is some common divisor of m and n. data structures and algorithms homework 1 fall 2019 — crn 41417 b. if the preconditions of gcd(m, n) are satisfied, then the value that the function returns is the greatest common divisor of m and n. hints: if d is a divisor of k, how can you rewrite k in terms of d? how do you show that two sets are equal?

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