As part of basic math and number theory, understanding the binary representation of a number divisible by four is an essential concept to grasp. Binary numbers consist of a sequence of 1s and 0s, and the last digit represents the remainder of the number divided by two. Knowing this, it thus follows that if a number’s binary representation ends in zero, then the number is divisible by two. By extension, if the binary representation of a number ends in 00, it is divisible by four.

For example, the decimal number 8 can be represented in binary as 1000. This is divisible by two as 1000 is divisible by two with a remainder of zero. Since the last two digits of the binary representation (00) are divisible by two, this means that the number is divisible by four, as 4 is a multiple of two.

We can also apply this concept to any other decimal number divisible by four. For instance, the decimal number 28 can be represented in binary as 11100. As before, the last two digits of the binary representation (00) are divisible by two, with a remainder of zero. This indicates that 28 is divisible by four, as 4 is a multiple of two.

The binary representation of any number divisible by four will therefore end in 00. This simple rule can be used to quickly identify whether a number is divisible by four without the need for complex calculations. If the binary representation of a number ends in 00, then it is divisible by four.