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?
2006-10-31 09:32:34 · 5 answers · asked by Laura 1 in Science & Mathematics ➔ Mathematics
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.
2006-10-31 09:54:38 · answer #1 · answered by Anonymous · 0⤊ 0⤋
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
2006-10-31 09:49:20 · answer #2 · answered by Up_In_Smoke 2 · 0⤊ 0⤋
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.
2006-10-31 09:56:03 · answer #3 · answered by rhino9joe 5 · 0⤊ 0⤋
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 -> 2*5*3
2006-10-31 09:49:40 · answer #4 · answered by ĞĦΘsŦŖiĐęŖ 2 · 0⤊ 0⤋
any non-prime number can be written as the product of primes.
examples: 50 = 5x5x2
117 = 3x3x13
80 = 5x2x2x2x2
2006-10-31 09:56:19 · answer #5 · answered by davidosterberg1 6 · 0⤊ 0⤋