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Write-up


Title
Dividing Primes

Problem Statement
How many of the first 100 positive whole numbers are divisible by all three of the smallest prime numbers?


Problem setup

Look at the numbers 1-100 to determine which are divisible by 2, 3, and 5.

 

Plans to Solve/Investigate the Problem

I will list the numbers 1-100 on a spreadsheet and eliminate those that do not fit the criteria.

 

Investigation/Exploration of the Problem

First I determined that the three smallest prime numbers are 2, 3, and 5.    My first thought was to multiply 2 * 3 * 5 to get 30.  I wondered if only multiples of 30 would answer the question.   Next I listed the numbers 1-100 on a spreadsheet and began to eliminate those numbers that were not divisible by all three.  By looking at each column, I deleted the first column, 1, 11, 21, etc. since they were not divisible by 2.  The second column, 2, 12, 22, etc. were not divisible by 5.  The same was true of the third column, 3, 13, 23, etc. and the fourth column, 4, 14, 24, etc.  The fifth column, 5, 15, 25, etc. was not divisible by 2.  The sixth column, 6, 16, 26, was not divisible by 5.  The seventh column was not divisible by 2, 3, and 5.  The eighth column, 8, 18, 28, etc. was not divisible by all three, as was true of the ninth.  Then only the 10 column was left, 10, 20, 30, etc.  Only 30, 60, 90 fit the criteria - divisible by 2, 3, and 5, so my initial thought was correct.

 

Extensions of the Problem

I never really considered whether the numbers in each column were divisible by 3 since most numbers were eliminated by trying to divide them by 2 or 5.  Only at the end was that really a concern.  Why?

Author & Contact
Vicki Hughes
vhughes@rockdale.k12.ga.us