Question 237034: what is the equation for36 and 48 prime fatorarization
Answer by solver91311(12126)   (Show Source):
You can put this solution on YOUR website!
I don't know what a "fatorarization" is. Be that as it may, there is no "equation" for performing the process of determining a prime factorization.
Step 1: Use your calculator to determine the square root of the number you want to factor. You only need to know the integer part, so just jot that down somewhere.
Step 2:
Divide by 2 as many times as you can. That is, divide your original number by 2, then divide the quotient by 2, then divide that quotient by 2, etc. Every time you can divide by 2 means there is a prime factor of 2.
Once you get to an odd quotient, check to see if you can divide by 3. You can divide by 3 if the sum of the digits is divisible by 3. For example 111 is divisible by 3, while 113 is not. If you can divide by 3, do it, and keep doing it as many times as possible. Every time you can divide by 3, you have a prime factor of 3 in your original number.
Once you can no longer divide by 3, try 5, then 7, then 11, and so on using every successive prime number as a divisor. The only question is how high in the list of prime numbers to you have to go with your trial divisors. The answer to that is found back at step 1. Once the next prime number in your list is larger than the square root of the number to be factored, you are done.
Rules for divisibility: Ends in 0 or 5, divisible by 5, but you won't be at this step unless your intermediate quotient ends in some odd number, so look for ends in 5.
http://math.about.com/library/bldivide.htm has a couple of tests for divisibility by 7, but they are so convoluted in my mind that just trying to divide by 7 is faster and easier.
Three digit numbers that are divisible by 11 have the property that the center digit is the sum of the two outer digits. (watch for a possible carry to the hundreds place)
Larger divisors are trial and error. If you have larger numbers to struggle with, I suggest you use one of several prime factorization calculators on the web -- mathwarehouse.com has one
Let's try this process with one of your numbers. 7 times 7 is 49, so you know that the square root of 48 is a little smaller than 7 and that the largest trial divisor you would ever have to use is 5. If you get that far, that is.
Divide by 2, equals 24. First factor of 2
Divide by 2, equals 12. Second factor of 2
Divide by 2, equals 6. Third factor of 2
Divide by 2, equals 3. Fourth factor of 2
Divide by 2, not an integer, therefore no more factors of 2.
3 is prime, One factor of 3, and you are done.
Hence the prime factorization of 48 is: 
Oh, and yes, spelling counts. It is all about you having the courtesy to take enough time and care in your written communications with someone who is trying to help you -- for free.
John
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