finding the correct sequence of factors?

Question

is there a way by which we can find the correct sequence of factors in a numbers

lets say 2 x 5 x 10 x 3 = 300

is there a way to decompose 300 into its orignal factors in the correct sequence?

thank you for your answers, let me explain a bit further.

i am not looking for prime numbers. i just want to know if its possible :
1 : find the correct multiples of that number e.g 2 x 5 x 10 x 3
2 : find the correct sequence eg 2,5,10,3

basically reaching the exact same sequence and numbers which resulted in 300.

I am looking for any possible way to go back from 300 to its orignal members, the operator doesnt really matter , it can be any operator or equation. as long as i can put in n numbers of elements (2 , 5 , 10 , 3) , get one number (300) , do some process and get the original numbers back.

Answer 1

No. Multiplication is commutative, which is to say that order doesn't matter at all. So there is no "correct" sequence without further information on how the sequence should be ordered.

Perhaps you are looking for the sequence of prime factors, but note that the factors you list are not all prime (namely, 10 = 5 x 2). In that case, the brute force way is to iterate through each prime number (2, 3, 5, 7, 11, etc.), checking to see if it divides evenly. If it does, add it to your factor list and start checking for more prime factors in the resulting quotient with the same factor you just added to your list (since you know nothing lower divides evenly and this factor may appear multiple times). For example:

300 / 2 = 150 --> Factor list: 2
150 / 2 = 75 --> Factor list: 2, 2
75 / 2 = 37.5 --> Not even, go to next prime
75 / 3 = 25 --> Factor list: 2, 2, 3
25 / 3 = 8.333 --> Not even, go to next prime
25 / 5 = 5 --> Factor list: 2, 2, 3, 5
5 / 5 = 1 --> Factor list: 2, 2, 3, 5, 5

When your reach 1, you're done. Note that this factor list matches yours except that the 10 is split into its prime factors 2 and 5.

If you don't restrict it to prime factors, the factors can be broken in a multiplicity of ways (e.g., 5 x 6 x 10 = 300, 2 x 15 x 10 = 300, etc. etc.), and there is no solution to the problem as stated.

Answer 2

I do not quite understand your query. If what you mean is the set of prime numbers that make up the number 300, follow this method:
Start dividing by the smallest prime, which in this case is the number 2, and continue to divide until you cannot use the number 2 any more. Then go to the next prime number, which in this case is the number 3. Then you go to the number 5, whci is the next higher prime number. Thus you get 2*2*3*5*5=300. Have I been helpful? Thank you for the question.

Answer 3

according to the commutative property of multiplication. the factors can be multiplied in any order, therefore every order is correct. 2 x 5 x 10 x 3 = 2 x 3 x 10 x 5 = 3 x 5 x 10 x 2 etc.

Answer 4

To find all the factors of 300 we need to divide the number by the lowest number divisible

1*300
2*150
3*100
4*75
5*60
6*50
10*30
12*25
15*20

Therefore all the factors in the correct sequence are starting from the left top 1,2,3,4,5,6,10,12,15 then starting from the bottom right 20,25,30,50,60,75,100,150,300

Answer 5

yes, first divide 300 by smallest positive number 2 . Then divide 150 again by the divisor 2 then divide 75 by the next smallest divisor 3 next divide 25 by the smallest divisor 5
thus 300=2x2x3x5x5 thus given any number we can finds its factors by dividing continuously by the smallest possible number.

Answer 6

300= 100 x3= 10x10x3= 2x2x3x5x5

Answer 7

It comes out 300 no matter which order you multiply them together so you could only guess at the original order.

Answer 8

yes , http://www.classbrain.com/artteach/publish/article_48.shtml should help , tells you the prime factors for a number
~~~