- #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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SUMMARY
The discussion focuses on calculating the number of prime factors of 360, specifically through prime factorization. The prime factorization of 360 is established as 360 = 23 × 32 × 5. From this factorization, it is concluded that the perfect-square factors of 360 are {1, 4, 9, 36}, totaling four perfect-square factors. The conversation also highlights the distinction between counting all prime factors and distinct prime factors.
PREREQUISITES- Understanding of prime factorization
- Knowledge of perfect squares
- Basic arithmetic operations
- Familiarity with exponent notation
- Learn methods for calculating prime factorization of larger numbers
- Explore the concept of perfect-square factors in number theory
- Study the properties of exponents and their applications
- Investigate algorithms for counting factors of a number
Mathematicians, educators, students studying number theory, and anyone interested in understanding prime factorization and its applications in identifying perfect-square factors.
- #2
Tide
Science Advisor
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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
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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
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
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
Last edited:
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