Number of Divisors an Integer Has


In this post we will learn how to get the number of divisors an integer has.

Sample problem 1:

How many divisors 6 have?


Listing all the positive divisors we have; {1,2,3,6} a total of four divisors. However if we are given large number it would be impractical and time consuming to list down manually the number of divisors.



Consider a positive integer N with prime factors ( ap)(bq)(cr). . . or

N=( ap)(bq)(cr). . .

Number of divisors = (p+1)(q+1)(r+1). . .

Let’s try the number 6.


Number of divisors= (1+1)(1+1)


Sample problem 2:

How many divisors are there in 8100?


Expressing 8100 to the product of its prime factor we have,

8100 = (22)(34)(52)

Number of divisors= (2+1)(4+1)(2+1)

= 45


Practice problems:
Direction: Determine the number of divisors the give number have.

1. 144

2. 343

3. 75600

4. 8x(9x)

5. a(a2)(a3). . .(a49)(b)(b2)(b3)(b4). . .(b49)


click here for answer key



Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.

Latest posts by Dan (see all)

You may also like...

54 Responses

  1. bkt 6 sa no. 2
    dpat 4

  2. bkt gnun ang sagot sa no.5.
    1 503 076 sagot q.

  3. kryptonj123 says:

    yup! it must be 4. I will make some corrections. Baka nalasing na ako diyan. Update ko nalang. XD

  4. kryptonj123 says:

    oh yes! I just noticed it. Sorry, wala ako calculator that time. Thanks! I appreciate your corrections

  5. suba me says:

    h2gYea You realize so much its almost hard to argue with you (not that I actually will need toHaHa).

  6. suba me says:

    ZCdfVb I think this is a real great blog.Much thanks again. Awesome.

  7. lucy ann says:

    ykK8L4 Thanks for sharing, this is a fantastic blog article.Really looking forward to read more. Really Cool.

  8. Enjoyed every bit of your post. Much obliged.

  9. dramacools says:

    This rather good phrase is necessary just by the way

  10. I value the article.Really thank you! Awesome.

  11. to your post that you just made a few days ago? Any certain?

  12. I think this is a real great blog post. Really Cool.

  13. May I simply say what a relief to discover somebody who

  14. Robot Vacuum says:

    Thank you for your article. Cool.

  15. Major thankies for the article.Really looking forward to read more. Want more.

  16. Thanks so much for the blog.Much thanks again. Really Cool.

  17. Natural says:

    running off the screen in Ie. I am not sure if this is a formatting issue or something to do with browser compatibility but I figured I ad post to let

  18. UoN says:

    My blog; how to burn belly fat how to burn belly fat [Tyree]

  19. bbw tube says:

    Thanks so much for the article.Thanks Again. Fantastic.

  20. This post is invaluable. When can I find out more?

  21. I value the article post.Much thanks again. Really Great.

  22. Muchos Gracias for your article post. Want more.

  23. Great, thanks for sharing this blog post.Thanks Again. Cool.

  24. handcuffs says:

    Im thankful for the article.Much thanks again. Keep writing.

  25. Say, you got a nice post.Much thanks again. Great.

  26. Very good info. Lucky me I ran across your blog by chance (stumbleupon). I have bookmarked it for later!

  27. Morovis says:

    Say, you got a nice article post.Thanks Again. Great.

  28. Friv says:

    Only wanna comment that you have a very decent website , I love the design and style it actually stands out.

  29. school says:

    Fantastic article post. Great.

  30. Major thanks for the post.Really looking forward to read more. Really Great.

  31. I was able to find good info from your articles.

  32. Just Browsing While I was surfing today I saw a great post concerning

  33. trenaplex says:

    736508 756875Greatest fighter toasts ought to entertain and supply prize on your couples. Initially audio system next to obnoxious crowd would be wise to realize 1 specific gold colored strategy as to public speaking, which is individual interests self. finest man jokes 212

  34. pest control says:

    This will be a great web site, might you be involved in doing an interview regarding how you developed it? If so e-mail me!

  35. Your posts constantly possess a lot of really up to date info. Where do you come up with this? Just saying you are very creative. Thanks again

  36. wow, awesome post.Really looking forward to read more. Really Cool.

  37. Enjoyed every bit of your blog post.Thanks Again. Much obliged.

  38. You have made some good points there. I looked on the net for additional information about the issue and found most individuals will go along with your views on this website.

  39. diy says:

    Thanks so much for the article.Thanks Again. Cool.

  40. Cathey says:

    Way cool! Some very valid points! I appreciate you penning this post and the rest of the website is also really good.

  41. online jobs says:

    Looking forward to reading more. Great post. Cool.

  42. Major thankies for the blog post.Thanks Again. Great.

  43. Im grateful for the article. Keep writing.

  44. Meryl says:

    Major thanks for the post.Really looking forward to read more. Cool.

  45. Im grateful for the article.Really looking forward to read more. Want more.

  46. Im thankful for the blog article.Much thanks again. Fantastic.

  47. A big thank you for your blog article. Awesome.

  48. You could definitely see your skills in the work you write. The world hopes for even more passionate writers like you who are not afraid to say how they believe. Always follow your heart.

  49. #mmj says:

    Very neat blog.Really looking forward to read more. Much obliged.

  50. The political landscape is ripe for picking In this current political climate, we feel that there as simply no hope left anymore.

  51. Thank you ever so for you article post. Much obliged.

  52. I really like and appreciate your article.Thanks Again.

  1. March 11, 2014

    […] exist that we never think of. The first topic I wrote about number theory is to find the number of divisors an integer has. This time let’s talk about finding the sum of those divisors without listing them […]

Leave a Reply

Your email address will not be published.