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Details for problem "GCD computation with the Euclidean Algorithm"

Quickname: 2001

Suitable for grades: Grade 5, Grade 6, Grade 7

Summary

Compute the GCD step by step with the Euclidian Algorithm.

Example


Description

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

Parameter
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

Remark
Description
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



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