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Numbers Ending With…

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.

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Numbers Ending With… -

Tag(s) : Arithmetics, Data Processing

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# Numbers Ending With…

## Numbers Ending with… Generator

### What it the end of a number? (Definition)

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.

### How to list numbers that ends with a given digit?

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)

### How to list multiples of some numbers?

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

### What is the name of numbers ending with '0'?

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.

### What is an automorphic number?

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 = 5776

Example: 625^2 = 390625

## Source code

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Cite as source (bibliography):
Numbers Ending With… on dCode.fr [online website], retrieved on 2023-10-01, https://www.dcode.fr/numbers-ending-with-some-digits

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