L1 · Divisibility by 2, 5 and 10

Learning goal

“I can decide whether a whole number is divisible by 2, by 5, or by 10 just by looking at its last digit - and I can explain why only the last digit matters.”

Divisible — a number is divisible by another if it divides into it exactly, with no remainder. 14 is divisible by 2; 15 is not.

Last digit (units digit) — the digit in the ones place: in 4,386 it is 6.

Even number — a whole number divisible by 2. It ends in 0, 2, 4, 6 or 8.

Factor — a whole number that divides another exactly. 5 is a factor of 35.

Worked example

Is 4,386 divisible by 2? Step 1: Split the number: 4,386 = 4,380 + 6. The 4,380 part is made of hundreds and tens - every hundred and every ten is even, so that part is always divisible by 2. Step 2: Only the last digit can block divisibility. The last digit is 6. Step 3: 6 is even, so 4,386 is divisible by 2. (Check: 4,386 / 2 = 2,193.) Say it plainly: hundreds and tens are always divisible by 2, so the 2-test is a test of the last digit only.

Check yourself — explain it

Why can we ignore all the digits except the last one when testing for divisibility by 2?

Paired problem — example still visible

Is 7,531 divisible by 2? -> No - the last digit, 1, is odd; the 7,530 part is fine, the 1 is left over.

Faded completion — last step is yours

"9,204: last digit is ___, which is even, so 9,204 ___ divisible by 2" -> 4; is

Ready to practise?

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

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