Factors are the numbers that can be grouped exactly to make a product. Multiples are the results you meet when you keep taking equal jumps. These ideas are not a list to memorize; they explain why some quantities can be shared evenly, why common denominators work later, and how to organize calculation choices.
MATH-102 · MODULE 05
Factors, Multiples, and Prime Structure
Use number patterns to organize products, divisibility, and efficient problem-solving.
A complete learning route
Build a method you can explain, not a string of answers to rush through.
This course begins each module with a teaching conversation, then moves through visible models, worked reasoning, connected practice, and a useful check. Use paper, counters, bottle caps, or a pencil line whenever a model helps.
Restoring this module…
Before you begin
Factors and multiples are a map of number relationships.
This module uses arrays and factor pairs to make the structure visible. A 24-item array might be 3 by 8 or 4 by 6. The total stays 24 while the arrangement changes. A prime number has only one row-by-column arrangement apart from reversing it, which is why it has only two factors.
Look for patterns, but prove them with a model or a division check. A divisibility clue is helpful because it tells you where to investigate; it is not a substitute for knowing what the quotient means. By the end, you will be able to explain a factor relationship rather than simply name it.
Start
See factors as rectangle pairs
Learning target
Factors are whole numbers that multiply to make a target number.
Arrays turn factor pairs into visible rectangles. Each rectangle has the same area but different side lengths.
Read or listen to the teaching conversation for this step
Module 5, Start
Transcript: Factors come in pairs. When two whole numbers multiply to make a target, they are factors of that target.
Guided practice
Work one idea at a time.
Each question comes after a model or explanation. A wrong response opens support and a chance to rebuild the idea; it never counts as complete.
Find a factor pair
Which pair is a factor pair for 24?
3 rows × 8 columns of squares
Server-scored mastery check
Show what you can do without a hint.
The server selects an original equivalent mastery set. A pass needs at least 80% plus evidence on the module’s central ideas.
Complete each guided-practice item correctly to open this mastery check. You have a safe path to every idea; a wrong practice response never closes the route.