When testing each prime, the " optimal " trial division algorithm uses all prime numbers not exceeding its square root, whereas the sieve of Eratosthenes produces each composite from its prime factors only, and gets the primes " for free ", between the composites.
42.
The division algorithm in Abu'l-Hasan al-Uqlidisi's 925AD book " Kitab al-Fusul fi al-Hisab al-Hindi " and in 11th century Kushyar ibn Labban's Principles of Hindu Reckoning were identical to Sunzu's division algorithm.
43.
The division algorithm in Abu'l-Hasan al-Uqlidisi's 925AD book " Kitab al-Fusul fi al-Hisab al-Hindi " and in 11th century Kushyar ibn Labban's Principles of Hindu Reckoning were identical to Sunzu's division algorithm.
44.
I have added the following as a footnote to the introductory sentence : Some widely-used textbooks, such as I . N . Herstein's " Topics in Algebra " and Serge Lang's " Algebra ", use " Euclidean algorithm " to refer to division algorithm.
45.
Every terminating decimal representation can be written as a decimal fraction, a fraction whose divisor is a 0.999 & } } and 1.584999 & } } are two examples of this . ( This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm .)
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