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This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient. Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend; for example, 10 / 3 leaves a remainder of 1, as 10 is not a multiple of 3.
n 5 n 4 n 3 4 4 0 s 4 s 3 s 2 4 4 4 1 But the same reasoning again applies to N' as applied to N, so the next digit of N' is 4, so s 2 and n 3 are also 4, etc. There are 5 divisions; the first four must leave an odd number base 5 in the pile for the next division, but the last division must leave an even number base 5 so the morning division ...
6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 1 / 4 , 1 1 / 5 , and 2 − 1 / 9 (i.e., 1 8 / 9 ). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.
The player to the right of the dealer is first dealt 3 cards then each next player (including the dealer) is dealt 2 cards at a time in an anti-clockwise fashion until each player has 14 cards except the player to the right of the dealer who should have 15. Any cards remaining with the dealer go on top of the stockpile.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Take each digit of the number (371) in reverse order (173), multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary (1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, ...), and adding the products (1×1 + 7×3 + 3×2 = 1 + 21 + 6 = 28). The original number is divisible by 7 if and only if ...
14 has an aliquot sum of 8, within an aliquot sequence of two composite numbers (14, 8, 7, 1, 0) in the prime 7-aliquot tree. 14 is the third companion Pell number and the fourth Catalan number . [ 2 ] [ 3 ] It is the lowest even n {\displaystyle n} for which the Euler totient φ ( x ) = n {\displaystyle \varphi (x)=n} has no solution, making ...
From this it follows that the rightmost digit is always 0, the second can be 0 or 1, the third 0, 1 or 2, and so on (sequence A124252 in the OEIS).The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS).