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

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5 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

  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 […]

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