Quote:
Originally Posted by mahalia  bear with me, i'm on the other side of the world so i just hope that our math terminologies are the same.
topsquark's post is very helpful, i didn't kow that first part! basically a prime number is something that has only two factors, being 1 and itself. our lovely mathematicians are always quarreling over whether or not 1 is prime, but when i last checked, one was not prime. just check with your teacher though. |
The definition of a prime natural number is: A natural number is prime if it has exctly
two distinct factors.
Suppose N is not prime then it does not have exactly two distinct factors.
Then it is either 1, which has only one distinct factor:-1, or it has more than
two distinct factors (as it must have at least two, 1 and itself).
Let a be the smallest proper factor of N, then:
N=a.b
for some integer b.
Suppose a>sqrt(N), then as b>=a a.b>sqrt(N).sqrt(N)=N a contradiction.
Therefore the smallest proper factor of a composite number N (composite
number: a non-prime with more than 2 distinct factors) is less than of
equal to sqrt(N).
RonL