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A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations In mathematics , a multiplication table (sometimes, less formally, a times table ) is a mathematical table used to define a multiplication operation for an algebraic system.
The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a ...
The squares contain a simple multiplication table. The first holds a single digit, which Napier called the 'single'. The others hold the multiples of the single, namely twice the single, three times the single and so on up to the ninth square containing nine times the number in the top square. Single-digit numbers are written in the bottom ...
[1] Every positive integer can be expressed as the sum of at most 19 fourth powers; every integer larger than 13792 can be expressed as the sum of at most 16 fourth powers (see Waring's problem ). Fermat knew that a fourth power cannot be the sum of two other fourth powers (the n = 4 case of Fermat's Last Theorem ; see Fermat's right triangle ...
This technique allows easy multiplication of numbers close and below 100.(90-99) [2] The variables will be the two numbers one multiplies. The product of two variables ranging from 90-99 will result in a 4-digit number. The first step is to find the ones-digit and the tens digit. Subtract both variables from 100 which will result in 2 one-digit ...
[2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of ...
The devices themselves don't use logarithms, rather they are tools to reduce multiplication and division of natural numbers to simple addition and subtraction operations. The first device, which by then was already popularly used and known as Napier's bones , was a set of rods inscribed with the multiplication table.
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