Question 11389: Hello!
I have 4 questions...
1) Is there a formula for finding all possible divisors for a particular number? For example how do I find all possible divisors for 386?
2) How do I find out if a number is a prime number? Is there a particular formula for that?
3) How do I express a number as a product of prime numbers?
For example, express 585 as a product of prime numbers.
4) Why is 5 x the square root of 3 + the square root of 27= 8x the square root of 3? Why isnt the answer 13.86? How do I change 13.86 into 8 x the square root of 3?
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! It seems that you rely too much on formulas. Yes, there are many formulas
in math but what important is the idea not the formulas. Formulas are
just for poople to memorize easily or for engineers to use, but they are not
real math.
1) Is there a formula for finding all possible divisors for a particular number? For example how do I find all possible divisors for 386?
Answer: There are no formulas for factorizataion of integers.
For 386 is even but not mulitple of 4 or 3
(since 86 is not amultipof 4 and 3+8+6 = 11 = 2 mod 3
so, 386 is not multiple of 3. Also, not a multiple of 11 why? ).
386 = 2 * 193
since sqrt(193) ~ 13.89, only need to try prime numbers 7< 13.
and we see 7 is not a divisor of 193.
Hence, 193 is prime and so 386 = 2 * 193 is the prime factorization of 386.
2) How do I find out if a number is a prime number? Is there a particular formula for that?
Answr: Again, no formula for primes. You can use sieve way to test if an given
integer is a prime. But the largest prime factor for an integer n is
<= sqrt(n) (why?)
There are many web sites you can refer about prime numbers ,as
http://dmoz.org/Science/Math/Number_Theory/Prime_Numbers/
3) How do I express a number as a product of prime numbers?
I don't know why you ask this question.
e.g. 585 = 5 * 117 = 3^2*5* 13
[117 is a multiple of 9 , why?)
For any give postive integer n, we just keep finding prime factors
until no more prime (smaller) factors (<= sqrt(n)) we can find.
4) Why is 5 x the square root of 3 + the square root of 27= 8x the square root of 3? Why isnt the answer 13.86? How do I change 13.86 into 8 x the square root of 3?
Forget your awful way of typing in regular English, you should type:
Why 5 sqrt(3) + sqrt(27) = 8 sqrt(3) ? [Or use some coding as Tex]
It is clear that
Hence,
= Why?
You had a very fatal error. That is , express the answer as
13.86 by using calculator to get the estimated value. Always remember
sqrt(3) is an irrational number the value you got from the
calculator is just the approximated value. And,there is no way for you to
change 13.86 to the irrational number sqrt(3). Of course,there is no need
to use any calculator to solve this kind of math questions.
Try to read and undrstand something about rational & irrational numbers
and do your best to get rid your wrong way of thinking about the abstract
great math as an engineer or businessman .
Kenny
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