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Divisibility by 4

November 10, 2011 GB High School Mathematics, High School Number Theory

This is the second post in the Divisibility Rules Series. In the last post, we discussed about divisibility by 2. In this post, we discuss divisibility by 4.

Now, how do we know if a number is divisible by $4$ ?

Four divides $100$ because $4 \times 25 = 100$ . It is also clear that four divides $200, 300, 400$ and all multiples of $100$ . Therefore, four divides multiples of $1000$ , $10 000$ , and $100 000$ . In general, $4$ divides $10^n$ , where $n$ is an integer greater than $1$ .

Now, how do we know if a number that is not a power of $10$ is divisible by $4$ . Let us try a few examples.

Example 1: Is $148$ divisible by $4$ ? $148$ is equal to $100 + 48$ and $100$ is divisible by $4$ . Since $48$ is also divisible by $4$ , therefore, $148$ id divisible by $4$ .

Example 2: Is $362$ divisible by $4$ ? $362$ is equal to $300 + 62$ . Now, $300$ is divisible by $4$ . Since $62$ is not divisible by $4$ , therefore, $362$ is not divisible by $4$ .

Example 3: Is $3426$ divisible by $4$ ? $3426 = 3400 + 26$ . Now, $3400$ is divisible by $4$ (it’s a multiple of 100), and $26$ is not divisible by $4$ . Therefore, $3426$ is not divisible by $4$ .

By now, you would have realized that we just test the last 2 digits of the numbers if we want to find out if it is divisible by 4: 148, 362, and 3426. » Read more

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