An **international identifier** is a number of different size which comes above or beside the national identification number and helps to identify a company over several countries in the world.

The main tools used as international identifiers are : EasyNumber, DUNS number, International Suppliers Network, European Business Register, international Business Identifier Code (BIC/ISO 9362, a normalized code for trade, especially popular in banking area as the international Bank_code - also known as Bank Identifier Code, Bank International Code and SWIFT code),...

**Mental calculation** comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper. People use mental calculation when computing tools are not available, when it is faster than other means of calculation (for example, conventional methods as taught in educational institutions), or in a competitive context. Mental calculation often involves the use of specific techniques devised for specific types of problems.

Many of these techniques take advantage of or rely on the decimal numeral system. Usually, the choice of radix determines what methods to use and also which calculations are easier to perform mentally. For example, multiplying or dividing by ten is an easy task when working in decimal (just move the decimal point), whereas multiplying or dividing by sixteen is not; however, the opposite is true when working in hexadecimal.

A **check digit** is a form of redundancy check used for error detection on identification numbers (e.g. bank account numbers) which have been input manually. It is thus analogous to a binary parity bit used to check for errors in computer-generated data. It consists of a single digit (sometimes more than one) computed by an algorithm from the other digits (or letters) in the sequence input.

With a check digit, one can detect simple errors in the input of a series of characters (usually digits) such as a single mistyped digit or some permutations of two successive digits.

The **Trachtenberg system** is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian Jewish engineer Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp. The rest of this article presents some of the methods devised by Trachtenberg. The most important algorithms are the ones for general multiplication, division and addition]*citation needed*[. Also, the Trachtenberg system includes some specialized methods for multiplying small numbers between 5 and 13.

The chapter on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.

- What 3 digit number with units digit to and hundred digit for is divisible by 9?
- What is the number if the tens digit of a 2 digit number is 1.5 times the units digit, and the sum of the digits is 5?
- What is a 5 digit whole number divisible by 5&6 that digit add up to 24 and the sum of the last 4 digits add up to 19 and the last 3 to 10 last 2 to 8 product?
- If the sum of the digits of a two digit number is 7 and the tens' digit is 3 more than the ones' digit, what is the number?
- What 5 digit number minus a 4 digit number equals 33333?
- What was the last digit to that number?
- What is the last digit of the number of pie?
- I am a 3 digit number. My 2nd digit is 4 times more than my 3rd digit. My 1st digit is 7 less than my second digit?

- The Fabulous Fibonacci Numbers - Scribd... the 2nd, 3rd, 5th ... that this sum is merely the product of the last number and the one that would ... 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18 ...
- Classical - Scribd... the second number is always lower than the first one. No number will ... the second number below the first one, last digits ... digit> {<digit>} .| + 0 | 1 | 2 ...