How Many Zeros Are There in n factorial

How many trailing zeros are there in 100! (! is read as factorial)? This is one of the most common problems in elementary school and middle school math competitions and for those who have memorized the strategy, this can be solved in less than five seconds. There are (100/5) + (100/25) = 24 trailing zeros in 100!. But why does the trick works?

Small Cases

Example 1: How many zeroes are there in 6!?

For those who are new to the factorial notation, when we say 6!, we mean that we multiply 6 and 5 and 4 all the way down to 1. That is

6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720.

So, where did all the zeros come from? Zero came from 5 multiplied by any even number factor. For example, in 6!,  if we multiply 6 and 5, this will give us 30, a number with one trailing zero. Notice that none of the remaining numbers in the multiplication can add another trailing zero. » Read more

7 Funny Math Comic Sites You Will Love

Mathematics is difficult to many, but it sometimes can be fun as well.  And luckily, there are creative and gifted people who never stop from making the subject light and funny. In this post, we look at some of the funny math sites on the web, particularly those who publish math web comics. Enjoy browsing the list!

1. XKCD – XKCD is a web comic of romance, sarcasm, and language. Among the three, I think sarcasm is the most successful (lol). In its home page, it says that “This comic occasionally contains strong language (which may not be suitable for children), unusual humor (which maybe unsuitable for adults), and advanced mathematics (which maybe unsuitable for liberal arts majors).” A web comic of sarcasm indeed.

2. (x,why?) – A math comic sites written by Chris Burke. The blog also contains some math jokes and also serious math sometimes. Mr. Burke usually allows bloggers to use his comics on blogs (I asked him two years ago) as long as you ask his permission. » Read more

Misconception About Venn Diagrams

Last year, I had a good discussion with some teachers about Venn diagrams. Several teachers commented that I should change the diagram below because it might give an impression that the number of rational numbers is the same as the number of irrational numbers. Sadly, I was not sure if I was able to explain my point. Anyway, below is an extended explanation to those comments.

Venn diagrams usually represent the logical relationships among sets. They do not concern with their cardinality (the number of elements). For example, if sets A and B have common elements, then their relationship can be represented by any of the three Venn diagrams below. In creating Venn diagrams, you do not represent if there is only one common element, or there are many: you are representing if there are common elements or  there are none. » Read more

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