L3 · Divisibility by 4, 6 and 8

Learning goal

“I can test divisibility by 4 (last two digits), by 8 (last three digits, or halving three times), and by 6 (passing BOTH the 2-test and the 3-test) - and I can say why each test works.”

Last two digits — the tens and ones digits: in 5,316 they form the number 16.

Last three digits — the hundreds, tens and ones digits: in 12,340 they form 340.

Halving — dividing by 2. Halving 96 gives 48.

Combined test — a test made of two simpler tests: 6 = 2 x 3, so the 6-test needs both the 2-test and the 3-test.

Worked example

Is 5,316 divisible by 4? Step 1: Split: 5,316 = 5,300 + 16. Every hundred is divisible by 4 (100 = 4 x 25), so the 5,300 part always divides evenly. Only the last two digits can block it. Step 2: Last two digits form 16. 16 / 4 = 4 exactly. Step 3: So 5,316 IS divisible by 4. (Check: 5,316 / 4 = 1,329.) The same idea stretches: every thousand is divisible by 8 (1,000 = 8 x 125), so for the 8-test only the last THREE digits matter. Alternative: halve three times - if you stay on whole numbers all three times, the number is divisible by 8, because 8 = 2 x 2 x 2.

Check yourself — explain it

For the 8-test we only check the last three digits because...

Paired problem — example still visible

Is 7,214 divisible by 4? -> Last two digits form 14; 14 / 4 = 3.5 -> No.

Faded completion — last step is yours

"5,120: last three digits form 120; 120 / 8 = ___, so 5,120 ___ divisible by 8" -> 15; is

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz