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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). If m is a divisor of n, then so is −m. The tables below only ...
A positive divisor of that is different from is called a proper divisor or an aliquot part of (for example, the proper divisors of 6 are 1, 2, and 3). A number that does not evenly divide but leaves a remainder is sometimes called an aliquant part of . An integer > whose only proper divisor is 1 is called a prime number. Equivalently, a prime ...
If the divisor has a fractional part, one can restate the problem by moving the decimal to the right in both numbers until the divisor has no fraction, which can make the problem easier to solve (e.g., 10/2.5 = 100/25 = 4). Division can be calculated with an abacus. [14]
Sociable numbers are the numbers in cyclic lists of numbers (with a length greater than 2) where each number is the sum of the proper divisors of the preceding number. For example, 1264460 ↦ 1547860 ↦ 1727636 ↦ 1305184 ↦ 1264460 ↦ … {\displaystyle 1264460\mapsto 1547860\mapsto 1727636\mapsto 1305184\mapsto 1264460\mapsto \dots } are ...
Note that although the above described conditions are necessary, they are not sufficient for a number to be highly composite. For example, 96 = 2 5 × 3 satisfies the above conditions and has 12 divisors but is not highly composite since there is a smaller number (60) which has the same number of divisors.
Numbers p and q like this can be computed with the extended Euclidean algorithm. gcd(a, 0) = | a |, for a ≠ 0, since any number is a divisor of 0, and the greatest divisor of a is | a |. [2] [5] This is usually used as the base case in the Euclidean algorithm. If a divides the product b⋅c, and gcd(a, b) = d, then a/d divides c.
First, take any number (for this example it will be 376) and note the last digit in the number, discarding the other digits. Then take that digit (6) while ignoring the rest of the number and determine if it is divisible by 2. If it is divisible by 2, then the original number is divisible by 2. Example. 376 (The original number) 37 6 (Take the ...
Regular numbers are numbers that evenly divide powers of 60 (or, equivalently, powers of 30). Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. As an example, 60 2 = 3600 = 48 × 75, so as divisors of a power of 60 both 48 and 75 are regular.