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admin | Category: Reverse Phone Lookup Usa | 29.06.2014
Or, numbers divisible by 2 are white while those with remainders after dividing by 2 get colored. Print a new triangle and test numbers to leave those divisible by 3 white and color those that are not divisible by 3. Some call these tricks but, as I alluded to in my last post, I distrust mindless tricks that lack deep understanding.
For now, I'll share the rule so that you can avoid all that division by three when you color the sheet. If the sum of the digits of a number is divisible by 3, then the number is also divisible by three.
So, 345 is also divisible by 3Let's look at the largest number in Pascal's triangle: 24,310.

Since we are coloring numbers that aren't divisible by 3, we would color triangles with 24,310.
Not only is it self-checking, but students get to make lovely patterns!Back to my pet peeves: sharing tricks with no reasoning to back them.
Both will be divisible by 3 or both will not divisible by 3 because the sum and the number are the same.It gets a little trickier with two-digit numbers. That would be so tedious, and it would take a long time unless you plugged it into a spreadsheet as I did below. It only took me 15 minutes to craft this spreadsheet to prove this divisibility test works for two-digit numbers.
Unfortunately, we must find a way to show the truth of the test for every number up through infinity.

We must show that, if the sum of the digits 7 + 8  is divisible by 3, then so is the number.78 = 70 + 878 = 63 + (7 + 8)Do you see it?
By pulling out one of the sevens, you end up with the sum of the two digits 7 + 8.78 = (9 x 7) + (7 + 8)Why am I making it uglier? Let's try it again to see if we can see the pattern.84 = 80 + 484 = 72+ (8 + 4)84 = (9 x 8) + (8 + 4)As always, 9 x 8 is divisible by 3 as is the sum, 8 + 4. Mine is in the spoilers (or it will be soon).Can you apply this idea to three-digit numbers?

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