The Ultimate Crash Course for STEM Majors Euclidean Algorithm and greatest common divisor free preview

Finding the Greatest Common Divisor with the Euclidean Algorithm – gcd(875, 4075)

This page is nothing more than a free preview of The Ultimate Crash Course for STEM Majors. This number theory lesson demonstrates the Euclidean Algorithm and determines the greatest common divisor of \(875\) and \(4075\), while preparing the sequence of equations used in the following problem.

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Then,

\[ 300=275(1)+(300-(1)(275)) \]

\[ =275(1)+25 \]

\[ \Rightarrow r_1=300,\qquad r_2=275,\qquad q_3=1,\qquad r_3=25. \]

Then,

\[ 300=25(12)+0. \]

By The Euclidean Algorithm, \(r_3=r_t=25\).

Thus,

\[ \gcd(875,4075)=25. \]

For Q2

\[ \begin{aligned} 4075 &= (875)(4)+575\\ 875 &= (575)(1)+300\\ 575 &= (300)(1)+275\\ 300 &= 275(1)+25\\ 300 &= 25(12)+0. \end{aligned} \]

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This lesson is nothing more than a free preview of The Ultimate Crash Course for STEM Majors. Continue with the series for additional worked examples involving the Euclidean Algorithm, greatest common divisors, number theory, algebra, calculus, differential equations, mathematics, physics, engineering, and other STEM subjects.

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