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The natural integer 6174 is known as Kaprekar's constant, [1] [2] [3] after the Indian mathematician D. R. Kaprekar. This number is notable for the following curious behavior: Select any four-digit number which has at least two different digits (leading zeros are allowed), Create two new four-digit numbers by arranging the original digits in a.
The units digit of plus the tens digit of . 1 + 7 + 3 + 2 + 4 + 5 + 4 = 26 {\displaystyle 1+7+3+2+4+5+4=26} carried from the third digit. The fourth digit of the answer is 6 {\displaystyle 6} and carry 2 {\displaystyle 2} to the next digit.
If the tens digit is odd, the ones digit must be 2 or 6. 40,832: 3 is odd, and the last digit is 2. The sum of the ones digit and double the tens digit is divisible by 4. 40,832: 2 × 3 + 2 = 8, which is divisible by 4. 5: The last digit is 0 or 5. [2] [3] 495: the last digit is 5. 6: It is divisible by 2 and by 3. [6]
Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits. Hexadecimal: Base 16, widely used by computer system designers and programmers, as it provides a more human-friendly representation of binary-coded values.
Digit sums and digital roots can be used for quick divisibility tests: a natural number is divisible by 3 or 9 if and only if its digit sum (or digital root) is divisible by 3 or 9, respectively. For divisibility by 9, this test is called the rule of nines and is the basis of the casting out nines technique for checking calculations.
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