What is the total number of divisors of 1728?

Find the number of divisors of 1728


Method:
Find  the prime factorization of the number n.
Take all the exponents in the factorization.
Add 1 to each
Then multiply these "exponents + 1"s together.

Solution:

Prime Factorization of 1728:

2 | 1728 
2 | 864

2 | 432

2 | 216  

2 | 108

2 | 54

3 | 27

3 | 9

3 | 3

   | 1

2^6, 3^3
Exponents: 6 & 3

Add 1 to each exponent (6+1) (3+1)
Multiple “exponents+1” together = (6+1) x (3+1) =7 x 4 = 28

Total number of divisors of 1728 = 28