The last digit of a multiple of 2 is an even number. The last two digits of a multiples of 4 is divisible by 4.

Being able to recognise multiples of the single-digit multipliers is very useful for lots of applied math questions. Multiples of 2 are easily recognised as “even numbers”, or number whose ones are divisible by 2. Since 10 is divisible by 2, any number of tens is even; therefore the test for divisibility by 2 relies only on checking the number of ones.

e.g., Is 376 a multiple of 2? Since 6 is an even number, the answer is “yes”

This idea is extended to the last two places when testing a number for divisibility by 4. Since 100 is a multiple of 4, the hundreds do not need to be tested. The multiples of 4 up to 40 or 48 should be memorized facts for students at this level. Two-digit numbers beyond this can be tested by dividing by 4 using an algorithm, or by halving twice.

e.g., Is 82 divisible by 4? We can halve 82, getting 41. But since 41 cannot be halved, we know that 82 is not divisible by 4.

Extending These Facts:

Students who recognise the reason why multiples of 2 have an even number of ones and multiples of 4 have a number of tens and ones which is a multiple of 4 may like to come up with a rule for divisibility by 8, or 16, or even 32. Alternatively, they could investigate rules for divisibility by 5 or 25.