More Theorems (err… Observations!)

Upon the recent “publication” of this blog, many people made mention of my “theorem” post. So here’s another one of the mathematical discoveries I failed to include in that post. Hehe enjoy sa mga readers ko haha!

My grade school Math teacher (forgot what grade that was) used to teach us that to test if a certain number is divisible by 3, you have to sum up the digits of that given number and if it sums up to a multiple of 3, then that number is divisible by 3. Thus, the number 87, whose digits sum up to 15, is divisible by 3. Similarly, the number 3,699,363,396 (adding up to 57, whose digits further add up to 12) is divisible by 3.

But why add if you can cancel?

Yes, I got this observation once again from my tricycle travels, jeepney journeys, and with the latest addition to the commuter’s collection: MRT misadventures. It sort of sprang out from the plate number additions I’m doing even until now. Anyway, this is just another method of divisibility test. The one our grade school teachers taught us is what I call the “addition method.” This, my brainchild (mwahahaha), is the “cancellation method” of testing the divisibility of numbers by 3.

Yup, instead of adding up the individual digits of 3,699,363,396, why not cancel all the digits that are already divisible by 3, which in this case is every single digit of the number: 3,699,363,396 (See? No need to add up the digits and waste neuron activity! You actually know that the number is divisible by 3 because every single digit is “duh-visible” by 3)

How about 10,326,962,001? Okay using cancellation, we take out the digits that are divisible by 3: 10,326,962,001. So the digits left are 1, 2, 2, and 1. However, adding these remaining digits gives you 6, which is divisible by 3. Therefore, without adding, you can say that 10,326,962,001 is indeed divisible by 3.

So, if one of these numbers are guaranteed to be divisible by 3:
a. 1,703,696,333
b. 2,820,039,615
c. 3,333,333,331
You would now know quicker.

Another method I observed is the “Power of Three” method (haha okay screw the Charmed Ones just this once!), where a certain number that has three digits which are repeating can instantly be acknowledged as divisible by 3, such as three hundred and thirty-three (333), one hundred and eleven (111), and yes, the lucky 888.

This goes for 111,111 (three elevens), 123,123,123 (three 123’s), and 878,787 (three 87’s).


Apparently, this is how bored I am. No actually, this is how BAD I need a break! Catch more of my life soon… I'll catch up first on it though.