10 points!!! How to find the prime factorization of 324?

......324
......./\
.....4...81..note 4 x 81 =324
.../..\... /\
.2.....2 9..9...4=2x2 81=9x9
........../\.../\
..2...2.3.3.3.3...9=3x3

the prime factor of 324 is 2 2 3 3 3 3

= 324
= 2 * 162
= 2 * 2 * 81
= 2 * 2 * 3 * 27
= 2 * 2 * 3 * 3 * 9
= 2 * 2 * 3 * 3 * 3 * 3 OR
= 2² * 3⁴

Answer: 2² * 3⁴

You need to divide the number by prime numbers, starting from the smallest which is 2.
S0 you will later end up with 2 x 2 x 81. 81 cannot be divided by 2, so divide it by the next prime number, 3.
You will end up with 2 x 2 x 3 x 3 x 3 x 3

324 is a composite number because it has factors other than 1 and itself. It is not a prime number.

The 15 factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324.
Note: There are an odd number of factors because 324 is a square number (18 x 18).

The factor pairs of 324 are 1 x 324, 2 x 162, 3 x 108, 4 x 81, 6 x 54, 9 x 36, 12 x 27, and 18 x 18.

The proper factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, and 162 or,
if the definition you are using excludes 1, they are 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, and 162.

The prime factors of 324 are 2, 2, 3, 3, 3, and 3.
Note: There is repetition of these factors, so if the prime factors are being listed instead of the prime factorization, usually only the distinct prime factors are listed.

The 2 distinct prime factors (listing each prime factor only once) of 324 are 2 and 3.

The prime factorization of 324 is 2 x 2 x 3 x 3 x 3 x 3 or, in index form (in other words, using exponents), 22 x 34.

NOTE: There cannot be common factors, a greatest common factor, or a least common multiple because "common" refers to factors or multiples that two or more numbers have in common.

324

2 162

2 81

3 27

9 3

3 3

Answer: 2^2*3^4

Hope this helps ya! :)

note that 324 is divisible by 2 or 3, let's divide first by 2:

324 / 2 = 162
and 162 is also div by 2:
162 / 2 = 81
81 is divisible by 3, so:
81 / 3 = 27
27 / 3 = 9
9/3 = 3
3/3 = 1

so the prime factors are 2 x 2 x 3 x 3 x 3 x 3

Pokemon Number 324

Check out my Math Variety blog posts on prime factorization for an explanation of this concept, practice problems, and solutions. Click on ads/links of interest:
http://mathvariety.blogspot.com/2009/04/prime-factorization.html
http://mathvariety.blogspot.com/2009/05/prime-factorization-practice-problems.html
http://mathvariety.blogspot.com/2009/05/prime-factorization-solutions-to.html

I also have an eHow article titled “How to Do Prime Factorization” at http://www.ehow.com/how_4776386_do-prime-factorization.html if you’re interested.

Prime factorization basically means to write a number as the product of prime numbers.

324 is:
2*(162)
2*(2*81)
2*2*(81)
2*2*(3*27)
2*2*3*(3*9)
2*2*3*3*(9)
2*2*3*3*(3*3)
2*2*3*3*3*3 (answer)

You could also write this as 2^2*3^4.

324 = 2 * 2 * 3 * 3 * 3 * 3
-- or --
324 = 2^2 * 3^4

To find the prime factorization of 324

324 = 2 * 162 = 2 * 2 * 81= 2 * 2 * 3 * 27 = 2 * 2 * 3 * 3 * 9
= 2 * 2 * 3 * 3 * 3 * 3 / 2² * 3⁴

it's simple.find the smallest prime number possible and another number that when multiplied,its product is equal to your number,which is 324.do the same method again to the number which was multiplied with the prime number.keep on doing this until you only have prime numbers left.remember!#one can never be used as a prime factor
example:324=162*2(2is the prime number). take 162and divide it.so 162=81*2.take 81 and divide it.81=27*3(81 isn't divisible by 2 so we use the next prime factor,which is 3)then 27=9*3,then 9=3*3(we cannot take 3 and divide since it is already a prime number).take the prime numbers you have used to multiply with,which are 2,2,3,3and 3.
multiply these numbers with each other which will equal to your number(324).so 324=(2 to the power of 2)*(3to the power of 3)this is your prime factorization of 324.got it?