Factors, multiples, and primes
Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems
Lesson
Set out your lesson
“Factors, multiples, and primes means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Counters or paper models for the idea
- Pencil for recording
Extra for the adult
Worked example. Adult shows one clear example for Factors, multiples, and primes, then the child tries a matching example with a reason.
Optional challenge. For Factors, multiples, and primes, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Factors, multiples, and primes, not mastery.
Share and support
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceFactors, multiples, and primes practice
Practice key ideas from Factors, multiples, and primes.
Free · no login · no ads · Practice answers and completion are not saved. Parent observation remains the lesson record.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
The Locker Game
Before you open · source notes
A locker-toggle story reveals factors, multiples, and square numbers. Use it for factor patterns, not every prime test.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk which locker numbers end open and what that says about factors. One pass does not prove every prime check.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “The Locker Game.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- List all factor pairs of 36: (1,36), (2,18), (3,12), (4,9), (6,6)
- State the first five multiples of 7
- Find the common factors of 24 and 36
- Find all common factors of 36 and 48
- Identify the first three common multiples of 6 and 8
- Determine whether a given number (e.g. 97) is prime and justify the reasoning
“Can your child list all the factor pairs for a number like 36 — (1, 36), (2, 18), (3, 12), (4, 9), (6, 6) — and find factors that two numbers share?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Multiplication & Division
- Age range
- Ages 9–13
Standards