Math · Stage 6

Test divisibility by 11 and by 125

Two detective tricks for big numbers — no long division needed. For 11, add and subtract the digits in turn. For 125, just read the last three digits.

✦ Math📘 Stage 6 · S6⏱ ~12 min🧒 Ages 10–12★ Free to start

I can test divisibility by 11 (alternating digit sum) and by 125.

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Kavi the Number Detective 🔍

A cashier shouts, "7293 stickers share evenly among 11 clubs — true or false?" The other owls reach for long division. Not Kavi! "Add the digits in turn: (3 + 2) − (9 + 7) = −11 — a jump of 11, so yes, it shares!" Then: "And 3625 ÷ 125? I only read the last three digits — 625 is on the list, so yes!" A good detective never divides the whole number — a clever test does the work.

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What your child will learn

1÷ 11 — the alternating digit sumYou never divide the whole number. Instead, add up the digits in the odd spots (counting from the right: the ones, hundreds, …) and add up the digits in the even spots (the tens, thousands, …). Find the difference. If it is 0 or a multiple of 11 (…−11, 0, 11, 22…), the number divides by 11. Tap a row.

2÷ 125 — read the last three digitsHere is why it is so easy: 1000 = 8 × 125, so every thousand is already a clean batch of 125. That means only the last three digits decide it. A number divides by 125 exactly when its last three digits make one of these eight endings. Tap a row.

3Sort each number into its boxNow use both tests. For each number, run the ÷ 11 alternating sum and check the ÷ 125 ending. Drop it in the box it belongs to — some pass neither test.

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A peek inside

Does 2728 divide by 11?

Odd spots (8 + 7) = 15, even spots (2 + 2) = 4. Difference 15 − 4 = 11 — a multiple of 11.

Try this at home: ÷ 11 test — find the alternating digit sum, then say pass or fail: 143 · 264 · 215

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

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Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.