- #1
shravan
- 16
- 0
how to calculate the number of prime factors of 360? please give the method
How to calculate the number of prime factors of 360?
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Discussion Overview
The discussion revolves around calculating the number of prime factors of the number 360, with initial inquiries about the method for this calculation. The scope includes both prime factorization and the identification of perfect square factors, leading to a clarification of the original question.
Discussion Character
- Homework-related, Mathematical reasoning, Conceptual clarification
Main Points Raised
- One participant asks how to calculate the number of prime factors of 360 and requests a method.
- Another participant suggests starting with the factorization of the number, indicating that it is not a difficult task.
- A third participant provides a partial factorization of 360 and questions whether the original poster meant the number of distinct prime factors or the total count of prime factors, including repetitions.
- The original poster later clarifies that they intended to ask about finding the number of perfect squares in 360 without factorizing the number.
- A subsequent reply states that the prime factorization of 360 is 360 = 2^3 * 3^2 * 5 and identifies the perfect square factors as {1, 4, 9, 36}, noting that there are four perfect-square factors.
- This participant also mentions a future intention to provide a mathematical method to calculate the quantity of perfect-square factors without factorization.
Areas of Agreement / Disagreement
Participants initially disagree on the interpretation of the original question regarding prime factors, but there is a shift in focus to perfect square factors. The discussion remains unresolved regarding the method to find perfect square factors without factorization.
Contextual Notes
The discussion includes a misunderstanding of the original question, leading to a shift in focus. There are also unresolved aspects regarding the method to calculate perfect square factors without factorization.
- #2
Tide
Science Advisor
Homework Helper
- 3,072
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HINT: Factor the number. :)
P.S. And, no, I am not being glib!
P.S. And, no, I am not being glib!
- #3
HallsofIvy
Science Advisor
Homework Helper
- 42,895
- 983
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).
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).
- #4
shravan
- 16
- 0
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.
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.
- #5
bomba923
- 759
- 0
That's a different question; prime factorization of 360 yields
[tex]360 = 2^3 3^2 5[/tex]
and therefore the only perfect-square factors included are
[tex]{\{1,4,9,36\}}[/tex]
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
[tex]360 = 2^3 3^2 5[/tex]
and therefore the only perfect-square factors included are
[tex]{\{1,4,9,36\}}[/tex]
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
Last edited:
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