The LCM of two numbers is 14 times their HCF, and the sum of the LCM and the HCF is 600. If one of the numbers is 280, find the other.

**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: $6\times 36=216=12\times 18$. ✓