Whole numbers: primes, GCF, and LCM

This is the last dedicated whole-number unit. Prime factorization should be automatic by now, written in index notation like 84 = 2² · 3 · 7. The greatest common factor is built from the primes two numbers share, each at its lowest power; the least common multiple uses every prime that appears, each at its highest power. Lists of factors and multiples still work for small numbers, but they miss things (GCF by listing and forgetting 12) and do not scale. The same unit revisits order of operations with nested grouping, because every later unit will evaluate expressions. On the AMC 8, GCF/LCM word problems — cycles that realign, ribbons cut into equal pieces — are regulars.