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.
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.
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.