DIVISIBILITY TESTS

what to read in a written number instead of dividing it: the tail, the digit sum and composite divisors

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

Formats: A4 · A3 · A2
What you get: Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject: maths · school · memo · classroom

The tests are grouped by where to look: the first six need only the last one, two or three digits, the next three fold every digit into one small number. The right-hand column shows what each test gives for the number at the top.

THE NINE TEST IS NOT ABOUT NINE

The digit sum catches nine not because nine is special but because we write in ten. Each place is worth exactly ten times the one to its right, and ten less one is nine; so a place may be replaced by its own digit without changing the remainder on division by nine.

Change the base and the divisor changes with it. In octal the same digit sum tests seven; in hexadecimal, fifteen. The alternating sum tests not eleven but the base plus one: nine in octal, seventeen in hexadecimal.

On the sheet

The tests are grouped by where to look: the first six need only the last one, two or three digits, the next three fold every digit into one small number. The right-hand column shows what each test gives for the number at the top.
Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
Nothing about how it was made: the sheet carries only what the reader needs.

Printing

Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
White background and sparing fills — it prints on a home printer without draining the cartridge.
Margins of at least 10 mm: a home printer cannot print to the edge.
No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 8 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

DIVISIBILITY TESTS

THE NINE TEST IS NOT ABOUT NINE

On the sheet

Printing

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