Prime factorsn Prime numbers
How many prime factors 15 has ? is it 1,3,5,15 or 1,3,5 or 3,5. Please explain the answer with reasoning. Note:1 is not a prime number nor a composite Thanks
addition ! 15 = 3* 5
So, the numbers less than and prime to 15 = 15 * 2/3 * 4*5 = 8
its not a sloution to your problem. just wanted to let you know
Rajorshi are you suggesting that there are 8 co-prime numbers of 15 which are less than 15.
I think you got the number 8 as 15 * (2/3) * (4/5) = 8 but sorry I could not follow it – Form where you got 2, 3, 4 and 5
What if the number has more than 2 prime factors, I mean say 210 = 2 x 3 x 5 x 7
yep sorry for the typo.
The one i was talking about is called the euler's function if i remeber it correctly. let me formally state the theorem.
if p1,p2,.....pr be the different positive prime factors of m , and Phi(m) denote the number of imtegers < m , that are prime to m , then
Phi(m) = m (1-1/p1)(1-1/p2).... (1-1/pr)
Thanks rajorshi
euler's function is something new for me.
After googling it I got few good articles and wrote down few points for my own purpose. Any one else interested can check it @ http://cat4mba.com/node/2003
1 is neither prime nor composite.
15 is not prime as it has 3 and 5 as factors.
15 = 3 * 5
Thus the prime factors of 15 are 3 and 5.