Proofs

Factoring and Multiples

Numbers

# Is there a direct way to determine the number of positive factors that a given number like 1800 has?

###### Wiki User

###### 2008-09-03 03:12:04

The easiest way is through easy websites such as this:

http://wiki.answers.com/Q/What_are_the_factors_of_math

Alternatively, you can use prime factorization. In this case,

1800 = 2*2*2*3*3*5*5. Thus any divisor contains at most three

factors of 2;

that means there are four possibilities: 0, 1, 2, or 3 factors

of 2. Similarly there are three possibilities for the number of

factors of 3 in a divisor, and the same for factors of 5.

Multiplying these together, we find there are 4*3*3 = 36 positive

integer divisors of 1800.

In general, take the exponents in the prime factorization, add

one to each of them, and multiply the resulting numbers

together.