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Details for problem "GCD computation with the Euclidean Algorithm"

Quickname: 2001

Suitable for K-12 grades: Grade 5 Grade 6 Grade 7

Elementary School, Primary School, Junior High School, Middle School, High School.


Compute the GCD step by step with the Euclidian Algorithm.


Compute the GCD step by step with the Euclidian Algorithm. (Beispiel für die Lösung)


The tasks is to perform a detailed calculation of the largest common divisor (GCD) of two whole numbers with the Euclidean algorithm. The number space from which the numbers are chosen is adjustable. Also the number of problens can be selected.

To perform the computation, the following steps are repeated in rounds according to the algorithm.

1. Determine the quotient and remainder of the larger and the smaller number.
2- If the remainder is zero, the GCD has been determined. It is the last quotient.
3. Select the divisor of this round as the dividend for the next round. The divisor for the next round will be the remainder of this round.
4. Repeat from step one with the new dividend and divisor.

The first problem can be configured as a sample problem, which will be presented with the solution.

Topics: Arithmetic Divisibility Puzzles

Tags: Division Multiplication Rules

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Customization options for this problem

Possible values
Number of problems
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Number range
50, 80, 100, 200, 500, 1000
Sample problem with answer
Yes, No

Similar problems

Name and direct link
Simpler approach to gcd: compare lists of factors to determine gcd
For two given numbers, the gcd and lcm are determined by comparing lists of multiples or divisors

dw-Math worksheet templates that do contain this problem

Greatest Common Divisor
Two ways to determine the gcd of two numbers.

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