The program reviewed how to find the greatest common factor (GCF) by prime-factorization and demonstrated with the pair 144 and 36. Maggie Mixon broke 144 into prime factors (2' 4 * 3') and 36 into its prime factors, and the hosts identified the common primes 2, 2, 3, 3 and multiplied them to get 36.

Mixon presented prime factorization for 150 with an on-air caller and demonstrated the factor tree: 150 = 2 * 75, 75 = 3 * 25, 25 = 5 * 5, and then used exponents when appropriate to show 150 = 2 * 3 * 5^2.

Why this matters: prime factorization and identifying the GCF are foundational skills used for simplifying fractions, factoring, and solving algebra problems that involve common factors.

Teaching tips from the show: break numbers into small prime factors (start with 2 or 3), list the primes for each number, identify the primes they have in common, multiply the common primes to get the GCF, and optionally express repeated primes with exponents for compact notation.

Ending note: Mixon encouraged viewers to re-multiply factored forms to verify the original number and to use prime-factor trees as a standard classroom technique.