LA 2100 · Quadrivium: The School of Arithmetic — Module 3: Factors, Cancellation and the Divisors

Led by James B. Thomson Simulacrum

Taking a number apart. Prime factorisation, cancellation, the greatest common divisor and the least common multiple — the six sittings that decide whether fractions defeat you.

1. Module 3

   Factors, Cancellation and the Divisors

   Led by James B. Thomson Simulacrum

   The question

   Six sittings, Thomson's pages 79 to 87. You will begin backwards,

   Outcome

   The student can resolve any number into its prime factors, abbreviate

   Sub-units

   1. ○ 3.1 Factors, Primes and Composites Open this unit → ✓ ↻
   2. ○ 3.2 Resolving a Number into its Prime Factors Open this unit → ✓ ↻
   3. ○ 3.3 Cancellation Open this unit → ✓ ↻
   4. ○ 3.4 Common Divisors and the Greatest Open this unit → ✓ ↻
   5. ○ 3.5 Multiples and the Least Common Multiple Open this unit → ✓ ↻
   6. ○ 3.6 Review, and What It Is All For Open this unit → ✓ ↻
   Begin the course → Print certificate of completion

   Practice scenarios

   The Class That Wants to Get On

   Your class has finished the four operations well and is impatient. They see no purpose in factoring, and three of the ablest have said so: they can already divide, so why six lessons on factors? One of them points out, correctly, that he can find the greatest common divisor by trying every number downward from the smaller one, and that this always works.

   Your goals

   • Answer the objection on its merits — trial descent does always work, and he is
   • not wrong
   • Find the case where trial descent becomes impractical, and let them meet it
   • Say what the module is for without simply telling them about fractions, which
   • they have not met
   • Decide whether to preview Module 4 as motivation, and defend it either way
   • Choose one thing to secure before advancing, and only one

   Practise this scenario →