How to calculate the number of prime factors of 360?

[shravan]

how to calculate the number of prime factors of 360? please give the method

 

[Tide]

HINT: Factor the number. :)

P.S. And, no, I am not being glib!

 

[HallsofIvy]

As Tide said: start factoring. It's not that hard. I'll get you started:

360= 2(180)= 2(2)(90)= ...
surely you can do the rest yourself. Did you mean number of distinct prime factors or just number of prime factors (i.e. counting "2" more than once).

 

[shravan]

sorry re question

I am sorry my question was wrong .however I wanted to ask how to find the no: of perfect squares in 360 without factorizing. I am sorry for sending the wrong question.

 

[bomba923]

That's a different question; prime factorization of 360 yields
360 = 2^3 3^2 5
and therefore the only perfect-square factors included are
{\{1,4,9,36\}}
from observing the prime factorization. There are only four perfect-square factors of 360.
(The "1" is trivial tho )

*Then again, I'll reply later when I'll write an explicitly mathematical way to calculate the quantity of perfect-square factors of 360-->without factorization, as you mentioned