Rylan T.

asked • 11/09/17

This one has me stumped, please help.

1*x*y*z= 663,552 what are the values for x, y and z?

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Kenneth S. answered • 11/09/17

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663,552 = 81 times 8192 so its prime factorization is 34213.
 
There are numerous choices of x, y and z; each would have base 2 or 3, and the total of exponent(s) on the 2s would have to be 13, and the total of exponent(s) on the 3s would have to be 4, in each case.
 
Mention ofthe factor 1 in front of xyz was totally needless.
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Rylan T.

Thank you for your answer but I see right off the bat the question has 4 components (1, X, Y, Z) and your response has 2 (34, 213) Don't know if that was intentional, also, I don't know much about prime factorisation. Is there a way to narrow down the possible answer even more?
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11/09/17

Kenneth S.

You need to understand more about factoring composite numbers. Every non-prime positive integer > 1 can be factored uniquely. I have done so for you with this particular large number.
 
The MEANING of what I stated has this effect: x,y,z could be 2,2, and 211•81, for example. Or 3,3,9•213. A very great number of possibilities exist; all you have to do is to use some power of 2 and 3 to make different combinations of values for x,y, and z, always being sure to use everything up from the stated prime factorization.
 
Your insistence on the 'fourth component', 1, is fatuous--since 1 is the multiplicative identity element, it is not conventionally written as a coefficient.
 
Just to show you another possibility:
x = 25   y = 27•24      z=24•3
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11/09/17

Rylan T.

Thank you for further explanation and detailed breakdown. Wasn't sure exactly how to read your value for Z but I put it in a calculator and got back a figure 345,028,186.7611≠663,552 apologies for being fatuous, I'd argue it's part genetics as I enjoy a balanced diet of greens, fibre and proteins. ??
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11/09/17

Elizabeth L. answered • 11/09/17

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You don't have enough information. The three numbers could be any three numbers that can be multiplied to get that answer. For example, I can multiply 6 * 4 to get 24, or 3 * 8. The product you show (663,552) is a multiple of 3, 4, 6, 8, and I'm sure many other numbers. So you have many possibilities.
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Rylan T.

Thank you for your answer. Could you suggest 3 numbers that might be a good fit for this equation? 
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11/09/17

Elizabeth L.

First - Other commentors seem to feel that your asterisks indicated exponents. Is that what you meant, or was that simply indicating multiplication?
Second, just play with it on a calculator. Take your product (663552) and divide it by 2 or 3 or 6 or whatever. When you get a whole number answer, do it again. (of course remembering or writing down what numbers you use) You'll have three numbers that will fit. Just for fun, see how many different combinations you can come up with. Tons of options!
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11/09/17

Elizabeth L.

Rylan, I may not have read one of your comments above very carefully. Are you trying to factor this down to prime numbers? If so, you have the short answers up there. If you're looking for the fourth integer, since your initial list includes (1), then it would also include (663,552). Aside from those two, it all comes down to twos and threes.
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11/09/17

Rylan T.

The astrix were supposed to represent multiplication symbols. So there are numerous numbers that could be multiplied to make 663552 right? Got you. Thank you for your answer.
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11/09/17

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