I need help with factoring 111,111,111.

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npowe05

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Aug 25, 2008
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I need help with factoring 111,111,111. Please help me and show work thank you
 
Re: Factoring....

You are the one who needs to show work. Start with the obvious and divide by 111.
 
Re: Factoring....

\(\displaystyle 111111111 = \left( {3^2 } \right)\left( {37} \right)\left( {333667} \right)\)
Now you show the work.
 
Re: Factoring....

The first thing I always look for is whether it is divisible by 2. Since your number does not end in an even number it is not divisible by 2. The next step is to see if it is divisible by 3. If the sum of the digits is a multiple of 3, the number is divisible by 3. So, I would divide by 3 until the obtained quotient is not divisible by 3. Next, is the result divisible by 5? The final digit must be a 5 or a 0 to be divisible by 5. Next I would try 7, then 11, then 13, etc. until I have a prime number left. So, get busy, and I'm sure you can do it.
 
Re: Factoring....

You are correct IF 3x3x37x333667 = 111,111,111 AND 3, 37 and 333667 are all prime numbers.
 
Re: Factoring....

How did you decide whether 333667 is a prime number or not?

If it is not a prime number - then you have to do further factoring.
 
Re: Factoring....

Loren said:
http://www.math.com/students/calculators/source/prime-number.htm
Click to expand...

I was trying to go towards the use of a spreadsheet and "sieve of Erasthonas" (Sp?).

\(\displaystyle \sqrt {333667} \, \le \, 600\)

and a list of all prime numbers less than 600 is easily available in the web.

It is an easy task to use a spreadsheet like excel and divide 333667 by every number in th list and confirm the primeness/compositeness of the number.
 
Re: Factoring....

or use command "print prmdiv(333667)" : 333667 :idea:
 
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