find the no of divisors of 10800?

Answer 1

The σ function is the "number of divisors" function. That is,
σ(n) = { # of divisors of n }

For a prime number p,
σ(p^n) = n + 1

One last important property of the σ function is that it is multiplicative; that is, σ(p^n q^m) = σ(p^n)σ(q^m).

All we have to do is obtain the prime factorization of 10800 to obtain the total number of divisors.

10800 = 100 x 108
= 10 x 10 x 9 x 12
= 2 x 5 x 2 x 5 x 3 x 3 x 3 x 4
= 2 x 5 x 2 x 5 x 3 x 3 x 3 x 2 x 2. Ordering this from smallest to biggest, we get
= 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5.

Putting this in the form of powers, we get
= (2^4)(3^3)(5^2)

Now, let's use that function.

σ(10800) = σ( (2^4)(3^3)(5^2) )
= σ(2^4)σ(3^3)σ(5^2)

And, as stated earlier, for a prime number p,
σ(p^n) = n + 1, so we get

= (4 + 1)(3 + 1)(2 + 1)
= (5)(4)(3)
= 60

There are 60 divisors of 10800.

Answer 2

10,800 = 108 * 100 = 108 * 4 * 25 = 4*27*4*25 = 16 * 27 * 25 =
= 2^4 * 3^3 * 5^2

What you need is the number of combinations of
2^m m=0,1,2,3,4 , there are 5 such numbers
3^n n=0,1,2,3, there are 4 such numbers
5^p p=0,1,2, there are 4 such numbers

The number of divisors is 5*4*3 = 60

Answer 3

Keep dividing it until you reach repeatable numbers, from 1 until sqrt(10800).

Answer 4

Amit Y is absolutely correct

Answer 5

do a prime tree....?