If I try to plug this into my calculator, I'll get something in scientific notation, because the answer is too big for the calculator to display. In practical terms, the calculator will show me the beginning of the number, and I'm only caring about the end of the number the "trailing" part. So the calculator won't help. I'll try expanding the factorial:. I know that a number gets a zero at the end of it if the number has 10 as a factor.
For instance, 10 is a factor of 50 , , and So I need to find out how many times 10 is a factor in the expansion of 23! Looking at the factors in the above expansion, there are many more numbers that are multiples of 2 2, 4, 6, 8, 10, 12, 14, That is, if I take all the numbers with 5 as a factor, I'll have way more than enough even numbers to pair with them to get factors of 10 and another trailing zero on my factorial.
Read the wiki page, you will learn something much more important than Math. Quantitative Aptitude — Number Systems — Q3 : The numbers 1, 2,…,9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value. Enroll Now. Download Unacademy App. Your email address will not be published. This site uses Akismet to reduce spam.
Learn how your comment data is processed. Number of trailing zeroes in a Product or Expression If we look at a number N, such that Number of trailing zeroes is the Power of 10 in the expression or in other words, the number of times N is divisible by When I am dividing N by 10, it will be limited by the powers of 2 or 5, whichever is lesser. Number of trailing zeroes is going to be the power of 2 or 5, whichever is lesser. Let us look at an example to further illustrate this idea.
Question 1: What is number of trailing zeroes in ? Question 2: Find out the number of zeroes at the end of N Looking at the expression, we can say that the power of 5 will be the limiting factor. All we need to do is to figure out the number of 5s in the expression.
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Last visit was: Nov 14, pm It is currently Nov 14, pm. Decision Tracker. My Rewards. So if we count 5s in prime factors, we are done. How to count the total number of 5s in prime factors of n!? For example, 7! It is not done yet, there is one more thing to consider. Numbers like 25, , etc have more than one 5. For example, if we consider 28! Handling this is simple, first, divide n by 5 and remove all single 5s, then divide by 25 to remove extra 5s, and so on.
Following is the summarized formula for counting trailing 0s. Trailing 0s in n! Following is a program based on the above formula: Attention reader! Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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