What is the role that primes play in the factorisation of numbers?

This is the answer we were given in our practise exam:





';Any composite number can be written as a product of prime numbers.';





But I still don't get it, can anyone explain it thoroughly and in basic elementary terms from scratch?What is the role that primes play in the factorisation of numbers?
Sure. Think about the definition of a prime number, it is a number that is divisible by itself and 1.





A composite number is a number that can be divided by some number besides it's self and 1.


On a side note, 1 does approximately nothing in factoring, a number multiplied by 1 is the number.





So if I take composite number, say 4, I can always rewrite it by factoring it until I get prime numbers (2*2).





another example, I take 9 and factor it by primes (in this case 3) until only primes are left, 9 = 3*3, both these numbers are prime and 9 can be rewritten as a product of them.





This will work for any none-prime number.


48 = 12 * 4 = 4*3*4 = 2 * 2 * 3 *2 * 2.What is the role that primes play in the factorisation of numbers?
A prime number is any number that has only two factors that is 1 and the number itself (ex. 7 = 1 x 7)





So say we had 24 which is composite we can first break it down to 1 prime and one composite number (2 x 12.....the 2 is prime and the 12 is composite) So from here you want to bring down the prime number and factor the composite 12 into to factors


so now we have the 2 x 2 x 6 ....so you have the same process to keep breaking down the composite numbers until they are all prime





FINAL ANSWER 2 x 2 x 2 x3 all the numbers are prime
A prime number is a number that is only divisable by one and itself...eg. 2. When you factor a composite #, you are trying to get it to its simplest, or prime numbers....eg. 30 -%26gt; 2*5*3
any non-prime number can be written as the product of primes.





examples: 50 = 5x5x2


117 = 3x3x13


80 = 5x2x2x2x2
A number is either prime or not. If not, it is at least the product of 2 factors and apply the rule above to each of the 2 factors, defining it as a ';number'; above. Eventually all the factors are prime.