# Inside Track: Multiples of 2 and 4

### Key Idea:

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.