How many of the first 100 positive whole numbers are divisible by all three of
the smallest prime numbers?
Look at the numbers 1-100 to
determine which are divisible by 2, 3, and 5.
Plans to Solve/Investigate the
I will list the numbers 1-100 on a
spreadsheet and eliminate those that do not fit the criteria.
Investigation/Exploration of the
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
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