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The significance of 16 or 32, which form the individual "signatures" of which a book is composed, is that they make the most efficient use of the paper used in the printing of a book. [1] If the number of printed pages in a book is, for example, 258, then the editor will attempt to move material from the two extra pages so that there will not ...
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m , for which n / m is again an integer (which is necessarily also a divisor of n ). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).
The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; [2] [3] this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4. If any number ends in a two digit number that ...
In mathematics, the amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, s ( a )= b and s ( b )= a , where s ( n )=σ( n )- n is equal to the sum of positive divisors of n except n itself (see also divisor function ).
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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.
The number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9, and 18 is divisible by 9.; The Hardy–Ramanujan number (1729) is a harshad number in base 10, since it is divisible by 19, the sum of its digits (1729 = 19 × 91).
The following is pseudocode which combines Atkin's algorithms 3.1, 3.2, and 3.3 [1] by using a combined set s of all the numbers modulo 60 excluding those which are multiples of the prime numbers 2, 3, and 5, as per the algorithms, for a straightforward version of the algorithm that supports optional bit-packing of the wheel; although not specifically mentioned in the referenced paper, this ...