prime factor of 23100?

You're asking me to do prime factorization. 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.

23,100 is:
2*11,550
2*(2*5,775)
2*2*(5,775)
2*2*(5*1,155)
2*2*5*(1,155)
2*2*5*(5*231)
2*2*5*5*(231)
2*2*5*5*(3*77)
2*2*5*5*3*(7*11)
2*2*5*5*3*7*11
2*2*3*5*5*7*11 <--- answer

2 x 2 x 3 x 5 x 5 x 7 x 11

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First of all, notice that 23,100 is an even number, so it's divisible by 2.

23,100 / 2 = 11,550 *** also even, so divide by 2:

11,550 / 2 = 5,775 *** ends in 5, so divide by 5:

5,775 / 5 = 1,155 *** divisible by 11:

1,155 / 11 = 105 *** divisible by 5:

105 / 5 = 21

= 3 x 7


Since 3 and 7 are both prime, you're finished dividing. Collect all your divisors:

2, 2, 5, 11, 5, 3, 7

Place them in order:

2, 2, 3, 5, 5, 7, 11

... and multiply them together:

2 x 2 x 3 x 5 x 5 x 7 x 11 = 23,100

The factors of a number are the numbers that can be multiplied together to give that number, or the numbers which divide exactly into the number (which comes to the same thing). Example: 1 x 12 =12 so 12 ÷ 1 = 12 2 x 6 = 12 so 12 ÷ 2 = 6 3 x 4 = 12 so 12 ÷ 3 = 4 So the factors of 12 are 1 2 3 4 6 12 Only two of these (2 and 3) are prime numbers (numbers which only divide exactly by themselves and 1) so it must be possible make 12 by multiplying 2's and 3's Here's how: 2 x 2 x 3 = 12 (NOTE 1 is NOT a prime number, mainly because you cannot build any new numbers by multiplying by 1 but also because it only has 1 factor, namely 1)) So the prime factors of 12 are 2 x 2 x 3 To find the prime factors of a number, start with the number and try and divide by 2. If that doesn't work, try and divide by 3, and so on with each prime number (2 3 5 7 11 13 etc). Do the divide sum, write the answer underneath and then try again and keep doing this until you get to 1. EXAMPLE: 42 ÷ 2 21 ÷ 3 7 ÷ 7 1 So prime factors of 42 are 2 x 3 x 7 EXAMPLE: 180 ÷ 2 90 ÷ 2 45 ÷ 3 15 ÷ 3 5÷ 5 1 So prime factors of 180 are 2 x 2 x 3 x 3 x 5 In case you are wondering "why bother?" being able to find prime factors of a number can be useful in problems involving fractions or ratios.

I think if you don't know the answer to this problem, you have (1) not understand what prime factorization is all about and that's okay because most people don't. (2) You don't know the division rules that were taught at an earlier grade.

divisible by 2 if it's even. A nubmer is 2 4 6 8 0 ending is divisible by 2 always!

divisible by 3 is when a number has the sum of its digits as divisible by a certain number. for instance 234567 is divisble by 3? Why because 2+3+4+5+6+7 = 27. And that is divisble by a certain number. This certain number is 3. 1234 is not divisible by 3 because 1+2+3+4=10 and 10 is not divisble by 3.

divisble by 4 is when the last two digits are divisible by 4.

48 is divisble by 4. Trial and error. Meaning you just got to try and see.

148 is divisble by 4. 248 is divisible by 4 1312937129783129748 is divisible by 4.

Why so? because 200 is divisible by 4. any x64 or xxxx86 is dvisble by 4 because x is represenint a 100 value. if x=2, then it's 200. 200 is always divisible by 4. 200 equals 2 times 100. 100 divided by 4 equals 25. 200 equals 2 * 100. 200 divided by 4 is 2 times 100 divided by 4. Is this divisible by 4? Yes! Because 200div4=2*100div4 = 2*25=50. 200div4 = 50. 248 is 200 + 48. 200 and 48 are both dividable by 4. Think of the funny number 17. 34 is divisible by 17. 17 is divisible by 17. so the multiples of 17 being 17 34 and then 51. 51 is divisible by 17 because it is a multiple of 17. 17+34=51 OR think of that as 17+(2)17=51 or 17+17+17=51.

Going back to xxxxxx48, x is just a multiple of 100. Any multiple of 100 is divisible by 4. The determining factor if the number is divided by 4 is if the last two digits can be disibile by 4.

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A number is divisible by 5 if well I'm not going to tell you. The list goes on and you should ask a teacher or something. Think about what I said and know that this stuff I am smart enough to understand I am also smart enough to know it's not really natural to think or digest. When I was in high school I got good grades. After high school with time to think, I came up with "revelations" and realize the school and the school teacher probably misses the point of all this.

In order to the find the prime factors of a number you find the 2 simplest factors.
The 2 simplest factors of 23100 are 100 and 231. From here you break it down till you can't break it down to it's simplest form as shown below

23100 = 100 x 231
100 = 5 x 20 231 = 11 x 21
20 = 5 x 4 21 = 7 x 3
4 = 2 x 2

The prime factors of 23100 are 5, 11, 5, 2, 2, 3, and 7. Multiply them together, gives you 23100. that means they are it's prime factors.
5 x 11 x 5 x 2 x 2 x 3 x 7 = 23100

Another way of doing this is my drawing a prime factor tree. you would have able to under stand it much easily and faster. unfortunately i am not able to draw one for you.

go to the website below to see how a prime factor tree looks like.

prime factor of 23100 are 2x2x5x5x3x7x11

first divide 23100 by 2
=23100/2 = 11550

again divide it by 2
=11550/2 = 5775

here 5775 is not divisible by 2 so try it by 3
=5775/3 = 1925

Now try by 5
=1925/5 =385

Again by 5
385/5 = 77

now 7 divides it exactly

77/7 = 11

therefore, 23100 = 2*2*3*5*5*7*11

100 x 231
2^2 x 25 x 7 x 33
2^2 x 5^2 x 7 x 11 x 3
2^2 x 3 x 5^2 x 7 x 11

23100 = 2 x 2 x 3 x 5 x 5 x 7 x 11
or
23100 = 2^2 x 3 x 5^2 x 7 x 11

Obviously 2 is a factor -divide through to get 11550
2 is another factor of this -- divide through to get 5775
Ends in a '5' so 5 is a factor -- divide through to get 1155
Again ends in '5' so 5 is another factor -- divide to get 231
Divisible by 3 -- devde to get 77
As 77 is 7 times 11

factors are 2x2x5x5x3x7x11

Hint -- the first number looks nasty. So spot the 'obvious factors' - -things
like 2 and 5 and divide them out. Hopefully then the number you are left with is much smaller and you can spot the answer from there