Posted: 1/11/2008 10:33:26 AM EDT
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I don't know how this question came into my head, but it's been driving me nuts since I can't figure it out. Is there a number, and if so what is it, which is divisible by every whole number between 1 and 10 (inclusively) which will result in an integer? _MaH Edited to clarify (x2) ETA - Just found out there is (using google - I cheated). See if you can determine it on your own! ETA 2 - Now that we've established there is, can you find the smallest number which will yield an accurate answer to the above question? |
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Yes, there is. Any number and every number, an infinity of numbers, can be divided by every number between one and ten. Of course, there are also an infinity of numbers betweeen one and ten, as well. I think you need to reformulate your question. Were you perhaps referring to integer values only, or what? |
Yep. Question clarified to reflect this. |
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i had to write some stupid program to do this in computer science, to teach us how to use the modulus function.. ETA: here it is in C #include <stdio.h> int main () { int x=1; int stop=0; int divisor, remainder; while ( stop != 1 ) { divisor = 1; remainder = 0; while ( remainder == 0 && divisor < 10 ) { divisor ++; remainder = x % divisor; } if ( remainder == 0 && divisor == 10 ) { printf("%i is divisible by 1 through 10", x); stop = 1; } else x ++; } return 0; } ANSWER: 2520 |
I am sure you meant to say "evenly" as in the result will be an integer. Yes, all you have to do to find that number is multiply all the numbers together that you want it to be evenly divisible by. 10! |
3.6288 million or 3,628,800 or 1x2x3x4x5x6x7x8x9x10 That is the easiest answer. divide by 10, and you have 362,880 which is still divisible by 10, so that is an answer as well. |
Neat....I didnt know that.... |
Ladies and gentlemen, we have a winner for finding the smallest number!  Prize is bragging rights  _MaH |
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There's probably lots of such numbers. The lowest one I come up with is 7,560. See, you don't need to 10!, because 6 is just 2x3, 8 is 2x4, and 10 is 2x5. So the low answer is 2x3x4x5x7x9. All you need to do is multiply the numbers in the series that aren't factors of each other for your answer. So, what do I win?? ETA: Scooped (and beaten) whilst typing my reply. |
You don't need 2 because 4 is already 2x2. You don't need 3 either, since 9 = 3x3. You do need 8 though, and 6 as well, I think. |
Negative. 8 = 2*2*2, 6 = 2*3 Really the only numbers you need are the primes (2, 3, 5, 7). If you breakdown 1 - 10 by their prime factors, and multiply the prime factors to the highest power, it'll look like this: 1 = 1*1 2 = 1*2 3 = 1*3 4 = 2*2 5 = 1*5 6 = 2*3 7 = 1*7 8 = 2*2*2 9 = 3*3 10 = 2*5 (2^3) * (3^2) * (5^1) * (7^1) = 8 * 9 * 5 * 7 = 72 * 35 = 2520 _MaH |
362,880 will work too. 15,120 |
Nice work, mhoffman! |
Show me a mathematical proof that this is correct and complete. |
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This is just finding LCM. Prime numbers is the key. Any whole number except 0 and 1 can be represented as multiples of prime numbers. so between 1 and 10, 2, 3, 5, 7 are the ones, so find combination of each prime numbers. The key is to find the most number of times each prime number shows up. 8 is 2*2*2 it has to be the one that shows up for 2. For 3, it is 3*3 and 5 and 7 comes out once, so the result is 2*2*2*3*3*5*7 = 2520. edit: doh! mhoffman did it FYI any other number that satisfies this requirement will be multiples of 2520
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