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?

Solution:

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.

 

FORMULA:

Consider a positive integer N with prime factors ( a^p)(b^q)(c^r). . . or

N=( a^p)(b^q)(c^r). . .

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

Let’s try the number 6.

6=2(3)

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

=4

Sample problem 2:

How many divisors are there in 8100?

Solution:

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. 8^x(9^x)

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

 

click here for answer key