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07 Jul 2016, 05:16
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Q--how many prime factors does r have if r/10 and r/15 is an integer?
10-> 2*5
15-> 3*5
does r have to be at least 2*3*5*5?
10-> 2*5
15-> 3*5
does r have to be at least 2*3*5*5?
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07 Jul 2016, 12:32
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r only needs one 5 in it's PF.
I consider the numbers one at a time and keep a running track of the minimum that I need:
In order for r/10 to be an int, r needs at least one 2 and one 5. So now we have 2*5.
In order for r/10 to be an int, r needs at least one 3 and one 5. We already have a 5, so this just adds a 3; now we have 2*3*5.
so 2*3*5 is the absolute minimum that must be in r's PF. You can confirm that his works; 2*3*5 = 30. 30 is a mult of both 10 and 15 and there is no smaller number that is a mult of both 10 and 15.
Hope this helps.
I consider the numbers one at a time and keep a running track of the minimum that I need:
In order for r/10 to be an int, r needs at least one 2 and one 5. So now we have 2*5.
In order for r/10 to be an int, r needs at least one 3 and one 5. We already have a 5, so this just adds a 3; now we have 2*3*5.
so 2*3*5 is the absolute minimum that must be in r's PF. You can confirm that his works; 2*3*5 = 30. 30 is a mult of both 10 and 15 and there is no smaller number that is a mult of both 10 and 15.
Hope this helps.
07 Jul 2016, 21:38
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ha15
You are thinking about successive division.
Say, r = 2*3*5*5
r/10 = 3*5 is an integer.
Now 3*5/15 = 1 is an integer.
This is when r must be at least 2*3*5*5 (you still can't say how many prime factors is has since 2*3*5*5*7*11 etc is also divisible by both 10 and 15)
But here, you are not given that r is divided successively.
r/10 = 2*3*5/10 = 3 (an integer)
r/15 = 2*3*5/15 = 2 (an integer)
So it is enough to have just a single 5. Only in case of successive division (when the 5 is canceled off in the first step) do you need two 5s. Since it is not mentioned that you need to divide success
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
