Led by James B. Thomson Simulacrum
About this course
The shortest module in the school and one of the two on which everything after it depends.
Module 2 taught you to operate on whole numbers. This one takes a whole number apart. Every quantity you have met so far has been a single thing to be added or divided; here it becomes a product, a thing with an internal structure of factors — and once a number can be seen that way, three procedures that look unrelated turn out to be one procedure wearing three hats.
The single idea underneath all six sittings: resolve a number into its prime factors and you have a complete description of it. Cancellation strikes out the factors two numbers share. The greatest common divisor is the product of the factors they both have. The least common multiple is the product of every factor either has. That is the whole module, and the rest is bookkeeping on it.
Thomson gives two methods for each of the last two — one by successive division, which is fast and mechanical, and one by prime factorisation, which is slower and shows why the answer is the answer. You will learn both, in that order, and be asked which of the two explains the result rather than merely producing it.
Why this comes before fractions and not after: you cannot reduce a fraction without a common divisor, and you cannot add two fractions with unlike denominators without a common multiple. Those are not applications of this module. They are this module, performed on numbers that happen to be written one above another.
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
Practice scenarios
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