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 ( ap)(bq)(cr). . . or
N=( ap)(bq)(cr). . .
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. 8x(9x)
5. a(a2)(a3). . .(a49)(b)(b2)(b3)(b4). . .(b49)
click here for answer key