# 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). . .**

Letâ€™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 = (2^{2})(3^{4})(5^{2})

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(a^{2})(a^{3}). . .(a^{49})(b)(b^{2})(b^{3})(b^{4}). . .(b^{49})

click here for answer key

### Dan

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