Teaching the kid how to factorize

So, one day when I return home, I find my wife desperately trying to teach the kid how to find all factors of a number in vain. The kid was unable to comprehend how to do it. After watching for a while, I decided to step in.

With the background in programming coming handy, I first explain what are prime numbers. Then, using the divide-and-conquer method, I show how to factorize.

For example, if the number is 36, I first say that the number itself and 1 are two of the factors.

36 = 36 x 1

Then, we choose a single factor which will divide the given number. For example, 9.

36 = 9 x 4

Now, repeat the above method for each of the factors until you reach prime numbers - numbers that cannot be factorized any further.

9 = 3 x 3
4 = 2 x 2

Since 3 and 2 are prime numbers, we are now in a position to find ALL the factors.

36 = 3 x 3 x 2 x 2

Now, form all possible combinations to get all the factors.

36 = 3 x (3 x 2 x 2) = 3 x 12
   = (3 x 3 x 2) x 2 = 18 x 2
   = (3 x 2) x (3 x 2) = 6 x 6


Add the ones found earlier, and that would complete the list of all the factors.

36 = 36 x 1
   = 9 x 4
   = 3 x 12
   = 2 x 18
   = 6 x 6

So, the factors of 36 are:
1, 36, 9, 4, 3, 12, 2, 18, 6

The above method has the advantage of being very fast, but it has the disadvantage that it becomes difficult if it is not easy to find the first factor.

A lesson in mathematics for a rickshaw driver

I had earlier written about how to compute the regular fare for the Mumbai autorickshaws. At the end of a rickshaw trip, I try to pronounce the fare computed from the meter reading. This usually impresses the rickshaw drivers. On a couple of occasions, I even tried explaining the mathematics to some of them.

Very recently, I found a rickshaw driver who was keenly interested in knowing this computation. When I explained the simple mathematics behind it, he was quite amazed. In fact, he was so grateful that he waived off a couple of rupees of the fare. I did not accept the reduction in fare, however, and paid the fare in full to the exact rupee.

Unfortunately, unlike for the regular fare, I was unable to come up with a curve fitting simple equation for the late-night (post-midnight) fare. Maybe I should've tried using a more advanced software such as MATLAB or Scilab or some other curve fitting tools.