Common factors and H.C.F.

If Q is the H.C.F. of P and Q,
then P is a multiple of Q and Q is a factor of P.
"P is a multiple of Q" and "Q is a factor of P" mean if P is divided by Q,
there is no remainder.

1. P is an integer multiple of Q.
2. P is divisible by Q.
3. P >= Q.
4. P/Q is a prime number.

Proof of 4:
If P/Q is not a prime number, there exists two intergers N and A such that
P/Q = NA or P/(NQ) = A,
i.e., P is divisible by NQ and NQ is also a common factor of P and Q.
Since NQ > Q => Q is not the H.C.F.

so P and Q has a mutiple rwlationship.