Divisibility Breakdown: Is 10 Always Divisible by 4?

If a number is divisible by 10, will it therefore be divisible by 4?

We begin by reviewing the divisibility rules:

• A number is divisible by 10 if and only if its last digit is 0. This implies that the number can be expressed as $10k$, where $k$ is an integer.
• A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For example, 112 is divisible by 4 because 12 (its last two digits) is divisible by 4.

Let's analyze these conditions:

Since any number that is divisible by 10 ends with a 0, examples would include 10, 20, 30, etc. Look at the last two digits of these numbers:

• For 10, the last two digits are 10, which is not divisible by 4 (since $\frac{10}{4} = 2.5$).
• For 20, the last two digits are 20, which is divisible by 4 (since $\frac{20}{4} = 5$).
• For 30, the last two digits are 30, which is not divisible by 4 (since $\frac{30}{4} = 7.5$).

From this analysis, it's clear that numbers like 10 and 30 are divisible by 10 but not by 4. Thus, it's possible for a number to be divisible by 10 without being divisible by 4.

Therefore, the answer to the question "If a number is divisible by 10, will it therefore be divisible by 4?" is no.