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September 11th, 2017, 02:56 PM  #1 
Newbie Joined: Sep 2017 From: uk Posts: 2 Thanks: 0  Making a question out of a number
Now this may seem like a very silly question to a lot of you. I was wondering whether it is possible in any way to take a long number  for example '25149193151512' and simplify it into a question  like '4^7 * 8^9'. Haven't studied maths for years so appreciate any help! Thanks very much. Last edited by skipjack; September 11th, 2017 at 03:13 PM. 
September 11th, 2017, 03:25 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,142 Thanks: 1417 
Do you realize that 4^7 * 8^9 = 2^(2*7) * 2^(3*9) = 2^41? 25149193151512 = 2³ × 3143649143939 
September 11th, 2017, 07:17 PM  #3 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,428 Thanks: 118 
Hey, this might be good for a new game!

September 11th, 2017, 09:48 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,891 Thanks: 716  
September 11th, 2017, 11:09 PM  #5 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,428 Thanks: 118 
Come on Denis McField, you are even playing my game even though it has reached 8000++ at this point.

September 12th, 2017, 01:50 PM  #6 
Newbie Joined: Sep 2017 From: uk Posts: 2 Thanks: 0  
September 12th, 2017, 04:54 PM  #7 
Senior Member Joined: May 2016 From: USA Posts: 823 Thanks: 335 
Well I still do not understand your question: make a question out of a number? What does that even mean? Any number can be expressed in terms of other numbers in an infinite number of ways. For example, 10 = 8 + 2 = 9 + 1 = 4 + 9  3, and so on. There is a theoretically and practically important way to analyze positive whole integers: each such number is prime or can be reduced to a product of primes in a unique way (disregarding order). There is a simple but lengthy algorithm for doing that. You need a table of primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc. You see whether the number can be divided evenly by 2. If so, you see whether that quotient can be divided 2. If not you try 3. Here is an example with a small number. 252 = 2 * 126 = 2 * 2 * 63 = 2 * 2 * 3 * 21 = 2 * 2 * 3 * 3 * 7. Completely mechanical. Last edited by JeffM1; September 12th, 2017 at 04:56 PM. 
October 20th, 2017, 11:39 AM  #8 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,820 Thanks: 750 
You can take any number you like and write it, in a unique way, as the product of its prime factors. I don't understand how you are then choosing to write as powers of nonprimes like "4" and "8". For this specific number, 25149193151512, since it is even, it is divisible by 2: 25149193151512= 2(12574596575756). That is also even so divide by 2 again: $\displaystyle 2^2(6287298287878 )$. Now, keep doing that to $\displaystyle 2^3(3143649143939)$. That is NOT even so does NOT have another factor of 2. It is easy to see that 3143649143939 is NOT divisible by 3, 5, 7, ... and other prime numbers up to 29: 3143649143939= 29(91165825174231) so $\displaystyle 24149193151512= 2^3(29)(91165825174231)$. Now look for factor, at least 29, of 91165825174231. 29 is again a factor! 91165825174231= 29(3143649143939) so $\displaystyle 25149193151512= 2^2(29^2)(3143649143939)$. Now look for prime factors of 3143649143939. Last edited by Country Boy; October 20th, 2017 at 11:42 AM. 

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