If p and q are two distinct prime numbers, then HCF(p, q) is:

**Theorem**: Every composite number can be expressed as a product of primes — UNIQUELY, up to the order of factors.

Example: $360=2^3\times 3^2\times 5$. There is no other set of primes whose product is 360.

**Consequences**:
1. **Finding HCF** by primes: HCF = product of LOWEST powers of common primes.
2. **Finding LCM** by primes: LCM = product of HIGHEST powers of all primes appearing.
3. **Identity**: HCF(a,b) × LCM(a,b) = $a\times b$.

Example: $a=12=2^2\cdot 3,b=18=2\cdot 3^2$. HCF = 2·3 = 6, LCM = $2^2\cdot 3^2=36$. Check: $6\times 36=216=12\times 18$. ✓