Tool to list numbers that satisfy a condition on their last digits in order to list all numbers (up to X) ending with some given digits.

Numbers Ending With… - dCode

Tag(s) : Arithmetics, Data Processing

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The end of a number is the digit or the list of digits composing its decimal writing.

For an integer, the last digit is the units digit.

For a finite floating point number it is the last digit of its finite decimal representation.

For a floating point number with non-finite decimal expansion, the number has no end.

To list numbers with the same end digits, it is possible to browse all the integers in ascending order and check their last digits. Another faster method is to browse these same integers and to concatenate the final digit(s) to it.

__Example:__ `5`, `15`, `25`, `35` are the first numbers ending with `5` (and therefore all numbers are multiples of 5)

Some digits positioned at the end of the number make it possible to deduce that the number is a multiple of N (under some conditions).

__Example:__ A number ending in `00` is necessarily multiple of 100 (but also 50, 25, 10, 5, and 2)

__Example:__ A number ending in `5` is necessarily multiple of `5`

__Example:__ A number ending in `0`, `2`, `4`, `6` or `8` is necessarily multiple of `2`

Numbers that end with one or more `0` are multiples of 10, sometimes called *round* numbers.

Mathematically speaking, a *round number* is different, it is an *integer* that does not have a decimal point nor decimal places, only an integer part.

An automorphic number is a natural integer $ n $ whose squared value $ n^2 $ ends with the same digits as the number itself.

__Example:__ `76^2 = 57 76`

__Example:__ `625^2 = 390 625`

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Cite as source (bibliography):

*Numbers Ending With…* on dCode.fr [online website], retrieved on 2024-10-04,

number,list,end,ending,digit,condition,multiple

https://www.dcode.fr/numbers-ending-with-some-digits

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