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What is GCD?

Anonymous

∙ 14y ago

Updated: 4/28/2022

GCD stands for "greatest common divisor".

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∙ 14y ago

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Is the square root of 6 an irrational number?

Yes it is. The proof is as follows:We prove the statement by contradiction i.e. Assume that sqrt(6) is a rational number.Then there exist positive integers p and q with gcd(p,q) = 1 such that p/q = sqrt(6).Square both sides: p^2 / q^2 = 6,p^2 = 6q^2.Now as 2 is a divisor of the right-hand side (RHS), it implies that 2 is also a divisor of the left-hand side (LHS).This is only possible if 2 is a factor of p.Let p =2k. Then k is a positive integer as well.Thus, 4k^2 = 6q^2,2k^2 = 3q^2.As 2 is a factor of the LHS, 2 is also a factor of the RHS.But this is only possible if 2 is a factor of q.=> gcd(p,q) >= 2. Contradiction!Thus sqrt(6) is irrational.yes it is

Related Questions

What is the gcd of 125 and 225?

GCD(125, 225) = 25 GCD(125, 225) = 25 GCD(125, 225) = 25 GCD(125, 225) = 25

What is Euclid's Algorithm?

Euclid's algorithm is a popular algorithm to compute the GCD of two numbers. Algorithm: Gcd(a,b) = Gcd(b, a mod b), where a>=b and Gcd(a,0) = a Say we want to find the GCD of 72 and 105. 105 mod 72 = 33, so GCD(72,105) = GCD(33,72) 72 mod 33 = 6, so GCD(33,72) = GCD(6,33) 33 mod 6 = 3 so GCD(6,33) = GCD(3,6) 6 mod 3 = 0 so GCD(3,6) = GCD(0,3) = 3. So the GCD of 72 and 105 is 3.

What is the GCD of 375 and 225?

GCD: 75

What is the GCD of 360 and 364?

GCD: 4

What is the GCD for 5767 and 4453?

GCD: 73

What is the GCD of 13 and 75?

GCD: 1

What is the gcd of 33 and 70?

GCD: 1

What is the gcd of 1296 and 1944?

GCD: 648

What is the gcd of 18 and 21?

GCD: 3

What is the gcd of 42 and 63?

GCD: 21

What is the gcd of 18 and 32?

GCD: 2

What is then GCD of 20 and 65?

GCD: 5

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