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September 11th, 2017, 01:56 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 02:13 PM. 
September 11th, 2017, 02:25 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1385 
Do you realize that 4^7 * 8^9 = 2^(2*7) * 2^(3*9) = 2^41? 25149193151512 = 2³ × 3143649143939 
September 11th, 2017, 06:17 PM  #3 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,312 Thanks: 114 
Hey, this might be good for a new game!

September 11th, 2017, 08:48 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,473 Thanks: 693  
September 11th, 2017, 10:09 PM  #5 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,312 Thanks: 114 
Come on Denis McField, you are even playing my game even though it has reached 8000++ at this point.

September 12th, 2017, 12:50 PM  #6 
Newbie Joined: Sep 2017 From: uk Posts: 2 Thanks: 0  
September 12th, 2017, 03:54 PM  #7 
Senior Member Joined: May 2016 From: USA Posts: 785 Thanks: 312 
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 03:56 PM. 

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