please help me find prime factors of 624?
962713
624/2 = 312\n312/2 = 156\n156/2 = 78\n78/2 = 39\n39/3 = 13\nThe prime factors are 2, 3 and 13\nThe prime factorization is 2^4 * 3 * 13
841724
Look at the prime factors of each number, first of all.\n\nThen take enough prime factors from each to get your LCM, like this:\n\nFind the LCM of 6, 18 and 30.\n\nSTEP 1:  Determine the prime factors of each:\n6 = 2*3\n18 = 2*3*3\n30 = 2*3*5\n\nSTEP 2:  Gather enough prime factors so that you have enough prime factors to generate each of your original numbers:\n\nFrom 6, take 2*3\nFrom 18, take another 3 (since you already have the 2*3 from 6)\nFrom 30, take 5 (since you already have 2*3)\n\nSTEP 3:  Put them all together:\nFrom step 2, we have 2*3*3*5 = 90\nTherefore, 90 is the LCM of 6, 18, and 30\n\nDid this example help?
890978
To get prime factors, keep dividing by numbers and divide those until you can't divide them no more!  For example,\n\n34 \n17 * 2\n\n(Can't divide 17 any more and can't divide 2 -- both of these are prime numbers)\n\nAnother example,\n\n120\n12 * 10\n2 * 6 * 2 * 5\n2 * 2 * 3 * 2 * 5 (<-- all prime numbers here)\n\nTry to get the rest yourself and post the answers, we'll tell you if you got them right!  ;-)
482620
All primes (ignoring 2) are odd.\n\nDivide odd numbers into 3 groups: those of the form 6n - 1, those of the form 6n + 1, and those of the form 6n + 3.\n\nIgnoring 3 itself, all primes are of the form 6n + 1 or 6n - 1, as all numbers of the form 6n + 3 or 6n - 3 are divisible by 3 and not prime. \n\nYour proposition follows from that fact.
807869
the prime factorization can be figured out by repeatedly dividing the number by a prime number.\n for example 12\n 12 divided by 2 = 6,   6 divided by 2= 3,  3 divided by 3= 1\n the answer is 1.\ni hope this was helpful.
46670
Factor trees are the way to go. Start with any composite number on the top of the page. Then think of any two factors of that number, then draw two branches downward from the first number to the two factors you determined. Then if either of the two numbers you chose are composite, find two factors of that number and draw two branches downward to the next level of factors. Keep doing this until the final row of numbers you get is all prime. Any prime factors that are repeated can be expressed with exponents.\n\nFor example, take the number 90:\nTwo factors of 90 are 9 and 10 (you can choose others if you wish).\nDraw two branches down from 90 to 9 and 10.\nBoth 9 and 10 are composites, so find factors for each of those. Factors of 9 are 3 and 3; factors of 10 are 5 and 2. Now our last line of prime factors is 3 x 3 x 5 x 2 or 3^2 x 5 x 2 (using exponents). And, BAM, there's our answer!\n\nVery crudely, your factor tree should look something like this (drawn without the branches):\n\n  90\n 10 9\n5 2 3 3
594189
34,\n\nYou are having the series as 2 times <prime numbers>\n2*2, 2*3, 2*5, 2*7, 2*11, 2*13, 2*17, 2*19, 2*23...\n = \n4, 6, 10, 14, 22, 26, 34, 38, 46 ...
614283
the first step is basically to factor 120175.  the obvious factor to do first is 5.  this gives us 5*24035.  then factoring another 5 gives us 5*5*4807.  since 4807 obviously isn't divisible by 5 or 2, try 3.  doesn't work - so keep on trying the next biggest prime number (1,2,3,5,7,11,13,17...)  turns out that 4807 is divisible by 11.  this gives us 5*5*11*437.  keep on going and you get 5*5*11*19*23.  just checking, yes - 5*5*11*19*23=120175.\n\nnow converting these factors into letters, you get the available letters EEKSW.  this can be rearranged to be WEEKS.  however, remember that 5*5*11*19*23 can also be written as 25*11*19*23, since this also equals 120175.  this means the word could also have KSWY.  but i don't think you can rearrange those letters to make a word.\n\nso therefore the english word encoded as 120175 is WEEKS.  basically, you factored the number, converted them into letters, and solved the anagram.\n\n[[edit]]\n\ninuyasha's right - there could be an infinite number of "a"s in there too since 5*5*11*19*23 = 5*5*11*19*23*1*1*1*...\n\nhowever, this gives us WEEKS+AAA... so using the online anagram solver, found at http://wordsmith.org/anagram/ , there are no words that have "WEEKS" in them and "A"s.  therefore, the answer is still WEEKS.
1165002
This is a wild guess.\n\n3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 = the number.\nThe answer will be the product of the first 12 primes that aren't 2. (If 2 were a factor, the answer would be even, not odd.)\n\nFor the rest, use a calculator. And check to make sure all those numbers are prime. Sorry this is such a whack answer.
83369
I am giving you a method which would minimize number of possibilities.\nFactorize the number of factors( in your example 9) in as many way as possible.( in your example 9 and 3*3)\nNow find out the possible numbers ( one for one factor combination) in following way ( we are going to have 2 numbers)\nThen all factor combinations are sorted so that largest one is in first place and lowest one in last place.\nFor a factor combination x1*x2*x3*...xn*...\nthe number will be \n2^(x1-1) * 3^(x2-1) * 5^(x3-1) * ... * pn(xn-1)...\nwhere pn is nth prime number.\nFor our two combinations,\nfor 9-> 2^(9-1)=256\nfor 3*3-> 2^(3-1) * 3^(3-1) = 36\nLowest of these numbers is our result. \nIn our example it is 36.\nLet us see another example lowest number with 12 factors.\n12 factorizes to 12, 4*3, 6*2, 3*2*2\nfor 12-> 2^(12-1)=2048\nfor 4*3-> 2^(4-1) * 3^(3-1) = 72\nfor 6*2-> 2^(6-1) * 3^(2-1) = 96\nfor 3*2*2-> 2^(3-1) * 3^(2-1) * 5^(2-1)=60.\nSo our answer is 60.\nThis method will be if the number of factor cobination  is too large. An way to get good answer( may not be correct) is to start from prime factorization and continue untill collecting first two terms into one causes better result.\n\nThat is in case of 12\nWe will start from 2*2*3 and get 60.\nThen test if 4*3 is better. If not we will take 60 as answer.( as it is 72 so we will).\nThis case we have correct result but modified version may not produce correct result.
1121426
I don't know if this is what you are looking for but simplified this fraction would be 24/43 (divided by 3). And you cannot simplify it any further because 43 is a prime number, as far as I remember...
499816
Factor each number into their prime factors.\nTake the greatest number of occurrences of each\nprime and use them and only them  as the factors of your answer.\n\n  For example 4 and 10. Primes for each are 2,2 and\n2,5. 2 occurs at most two times and 5 occurs at most\nonce. So the factors in your answer are 2,2,5\nand the answer is 20. \n  Concise but complete. Exhaustive but exclusive.\nThat's elegance.
84784
You should really just draw out the factor tree.\n\nYou will get 2power4 times 3 in prime factorization.\n\nYou just find the lowest prime number and a multiple and branch down the tree in the same process. Also bring down the primes. Once you have all prime numbers you put them together them to get the prime factorization.\n\nHere is the tree:\n\n                             48\n                            /  &#92;\n                           2 * 24\n                          /   /  &#92;\n                         2 * 2 * 12\n                        /   /   /  &#92;\n                       2 * 2 * 2 *  6\n                      /   /   /    / &#92;\n                     2 * 2 * 2  * 2 * 3\n\n                             2^4 * 3
1138566
Have a look at http://alumnus.caltech.edu/~chamness/prime.html - it's a Java prime number generator with source code
120534
No, prime numbers are numbers that cannot be divided by anything but itself and 1. 6, 12, 24, and 36 can all be divided by 2
875190
Perform a prime factorization of each number:\n16 = 2 x 2 x 2 x 2\n36 = 2 x 2 x 3 x 3\n\nTo find the lowest common multiple, you need to take each prime factor, enough to cover both numbers.  In other words you need four of the 2s and two of the 3s.\n\nLCM(16, 36) = 2 x 2 x 2 x 2 x 3 x 3\nLCM(16, 36) = 144\n\nThe other people might be thinking greatest common factor, but even that answer is wrong since the GCF(16, 36) is 4, not 2.
813306
Start by dividing by 2 until you can't divide by 2. Then 3, then 5 etc..(prime numbers) until your number has been divided so many times that it equals 1.\n\nThe product is the number you divided into\n\nEg\nExpress 24 as product of primes\n\n24 / 2 =12\n12/2 =6\n6/2 =3\n3/3 =1\n\nThe prime productes are 2, 2, 2, 3\n\nSo you express it as 2^3*3\n\nNow do the same with 252