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Add the digits in blocks of two from right to left. The result must be divisible by 11. [2] 627: 6 + 27 = 33 = 3 × 11. Subtract the last digit from the rest. The result must be divisible by 11. 627: 62 − 7 = 55 = 5 × 11. Add 10 times the last digit to the rest. The result must be divisible by 11. (Works because 99 is divisible by 11).
A shutdown valve (also referred to as SDV or emergency shutdown valve, ESV, ESD, or ESDV; or safety shutoff valve) is an actuated valve designed to stop the flow of a hazardous fluid upon the detection of a dangerous event. This provides protection against possible harm to people, equipment or the environment.
4: penultimate digit is odd (2n+1), final digit is {2, 6}; or penultimate digit is even (2n), final digit is {0, 4, 8}. 3: sum of all digits is a multiple of 3. 9: sum of all digits is a multiple of 9. 6: an even number that passes the divisibility test for 3. 11: sum of digits in even places and sum of digits in odd places differ by a multiple ...
A proof test is a form of stress test to demonstrate the fitness of a load-bearing or impact-experiencing structure. An individual proof test may apply only to the unit tested, or to its design in general for mass-produced items. Such a structure is often subjected to loads above those expected in actual use, demonstrating safety and design margin.
Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from prime's square). In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit.
The addition, subtraction and multiplication of even and odd integers obey simple rules. The addition or subtraction of two even numbers or of two odd numbers always produces an even number, e.g., 4 + 6 = 10 and 3 + 5 = 8. Conversely, the addition or subtraction of an odd and even number is always odd, e.g., 3 + 8 = 11. The multiplication of ...
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.
Using fast algorithms for modular exponentiation and multiprecision multiplication, the running time of this algorithm is O(k log 2 n log log n) = Õ(k log 2 n), where k is the number of times we test a random a, and n is the value we want to test for primality; see Miller–Rabin primality test for details.