Prime Factorization Homework Problem 2

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Homework Help Overview

The problem involves determining the year a senator elected during the presidential election year of 2000 would campaign again during a presidential election, considering the election cycles of both presidential elections and senatorial elections.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the election cycles of 4 years for presidential elections and 6 years for senatorial elections. Some suggest using a table of values or finding the lowest common multiple through prime factorization.

Discussion Status

There are various interpretations of the problem, with some participants providing different answers based on their reasoning. Guidance has been offered regarding the use of prime factorization to find the least common multiple, but no consensus has been reached on the final answer.

Contextual Notes

Participants note the lack of additional information and express uncertainty about their mathematical skills, which may affect their interpretations and approaches to the problem.

shawonna23
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Homework Statement


Presidential elections are held every four years. Senators are elected every 6 years. If a senator was elected in the presidential election year of 2000, in what year would he or she campaign again during a presidential election year?



Homework Equations


dont know how I would show the answer using factorization

2000+6=2006 2000+4=2004+4=2008

The Attempt at a Solution


2008
 
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We need more information on this one. Anyway, try making a table of values starting with year 2000. Again, this seems to be a lowest common factor problem. There is a 4 and a 6, so ... ? ...!
 
This was all the information I was provided for that question. Do I have the correct answer?
 
Ok, same caveat (not very good at math), but here's what I think:

2012.

Here's how I arrived at that.

i) Forget the 2000s, they are just confusing. Since it starts at 0, just focus on the 4 and the 6. A president gets elected every 4 years & a senator every 6 years.

ii) Find the lowest (least?) common multiple of 4 and 6 by prime factoring each one.

4 = 2 * 2​
6 = 3 * 2​

iii) Since there are 2s in both groups, circle the largest grouping of 2s (4 = 2*2) and not the other one.

iv) Multiply all the circled prime factors (2*2*3) and you get 12.

v) Draw a chart to check the answer.
 
Look for their lowest common multiple. And that number is 12.

2000 + 12 = the year 2012
 

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