Euclidean Algorithm

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Julien Ugon

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Julien Ugon 3 years, 9 months ago

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Question statement

Apply the Euclidean algorithm to find the greatest common denominator between {pq[0]} and {pq[1]}. Show the steps.

Give any introductory information the student needs.

			Name	Type	Generated Value

r0	integer	10
m1	list	[ 6, 2, 3, 6 ]
pq	list	[ 2830, 450 ]

			Name	Type	Generated Value

euclid	list	Nested 4×4 list
g	matrix	Matrix of size 4×4
l	number	127350
prefill	list	[ "", "", "", "" ]

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Number of elements in the array.

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

→ Used by:

Matrix entry

Ask the student a question, and give any hints about how they should answer this part.

Please enter all the steps of the Euclidean algorithm below starting from the numbers {pq[0]} and {pq[1]} (please enter the number of steps you need in the "Rows:" box.)

Marks

Correct answer

xxxxxxxxxx
 
g

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Advanced settings

Number of rows

Number of columns

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(No limit)

Minimum number of columns

Maximum number of columns

Margin of error allowed in each cell

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Precision restriction

Allow the student to enter fractions?

Display numbers in the correct answer as fractions?

Pre-filled cells

xxxxxxxxxx
 
[[pq[0],"",pq[1]]]

Advice

In order to apply the Euclidean algorithm to find the gcd, you need to apply integer division repeatedly, until the remainder is 0.

Once you know the gcd between two numbers $p$ and $q$ you can find their lcm using the following formula:

$\mathrm{lcm}(p,q) = \frac{p\times q}{\mathrm{gcd}(p,q)}$

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Number entry
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This question is used in the following exams:

Number Theory (Core) - paper test by Julien Ugon in Discrete Mathematics.
Number Theory (Core) by Julien Ugon in Discrete Mathematics.
Practice Number Theory by Julien Ugon in Discrete Mathematics.

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Euclidean Algorithm

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Julien Ugon 3 years, 9 months ago

Julien Ugon 3 years, 9 months ago

Julien Ugon 4 years, 10 months ago

Julien Ugon 4 years, 10 months ago