Every whole number greater than 1 is either prime or built from primes. Breaking it into those primes is its prime factorization, and a factor tree finds it by splitting the number into factors again and again.

The factorization is unique: however you split, 60 always ends as 2 × 2 × 3 × 5. Once you have two numbers' primes, they give the greatest common factor (the shared primes at their lowest powers) and the least common multiple (every prime at its highest power).