SOLUTION: write 6750 as a product of prime numbers using exponents

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Question 1185265: write 6750 as a product of prime numbers using exponents

Found 3 solutions by Edwin McCravy, MathLover1, greenestamps:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
6750 = (2)(3375) = (2)(3)(1125) = (2)(3)(3)(375) = (2)(3)(3)(3)(125) =

(2)(3)(3)(3)(5)(25) = (2)(3)(3)(3)(5)(5)(5) = 2%2A3%5E3%2A5%5E3

Edwin


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

6750=2%2A3%5E3%2A5%5E3+ ....->(7 prime factors, 3 distinct)

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Presumably, in posting this question, you were interested in learning HOW to work the problem.

One of the responses you got doesn't help at all with that, since it just shows the answer.

The other response is inefficient, as it takes out one small prime factor at a time.

The solution is reached more easily by breaking the number into larger identifiable factors and then further simplifying those factors.
6750
(675)(10)  the factor of 10 is easy to see
(27)(25)(10)  I recognize 675 as a multiple of 25; if you don't see that immediately, you can take the two factors of 5 out one at a time
(3*3*3)*(5*5)*(2*5)  the previous three factors are all quickly and easily decomposed into prime factors

ANSWER: (3^3)(5^3)(2^1)