Fundamental Theorem of Arithmetic & Parity

AMT 7, Summative Test 2 Review Quiz

40 items. Pick one answer per item; you’ll see right away if it’s correct, along with the solution. Scratch paper is allowed.

n = p₁^a₁ × p₂^a₂ × … × p_k^a_k

Every integer n > 1 has exactly one prime factorization (order aside).

GCF × LCM = a × b

GCF: common primes, lowest powers. LCM: all primes, highest powers.

n ≡ r (mod 2), r ∈ {0, 1}

r = 0 → even (n = 2k); r = 1 → odd (n = 2k + 1)

E + E = E, O + O = E, E + O = O

E × any = E, O × O = O

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