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# hexadecimal

The hexadecimal system is a positional number system with base 16, using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. It offers a compact way of expressing binary numbers.

In hexadecimal, all Mersenne numbers greater than 127 end with the digit F repeated several times, while all Fermat numbers greater than 17 are written with several significant zeroes book-ended by two 1’s.

The term hexadecimal is a mixed formation of a Greek begin and a Latin end. There is also a less used synonym hexadecadic of purely Greek derivation.

Some divisibility tests in hexadecimal are:

$n$ is divisible by 2 if its least significant digit is 0, 2, 4, 6, 8, A, C or E.

$n$ is divisible by 4 if its least significant digit is 0, 4, 8 or C.

$n$ is divisible by 8 if its least significant digit is 0, or 8.

$n$ is divisible by 15 if it has digital root F.

$n$ is of course divisible by 16 if it ends in a 0.

$n$ is divisible by 17 if the difference of the odd placed digits and the even place digits of $n$ is a multiple of 17.

## Mathematics Subject Classification

11A63*no label found*

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