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a perfect number equals the sum of its proper divisors; ... 6, 7, 14, 21, 42 8 96 54 abundant, highly abundant, composite 43: 1, 43 2 44 1 deficient, prime 44:
The division of two whole numbers does not necessarily result in a whole number. For example, 1 divided by 4 equals 1/4, which is neither even nor odd, since the concepts of even and odd apply only to integers. But when the quotient is an integer, it will be even if and only if the dividend has more factors of two than the divisor. [6]
The number of divisors of 96 is 12. [6] As no smaller number has more than 12 divisors, 96 is a largely composite number. [7] Skilling's figure, a degenerate uniform polyhedron, has a Euler characteristic = Every integer greater than 96 may be represented as a sum of distinct super-prime numbers.
Illustration of the perfect number status of the number 6. In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number.
For example, the "primitive" friendly pair 6 and 28 gives rise to friendly pairs 6n and 28n for all n that are congruent to 1, 5, 11, 13, 17, 19, 23, 25, 29, 31, 37, or 41 modulo 42. [ 6 ] This shows that the natural density of the friendly numbers (if it exists) is positive.
The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. If no exponent is written then the multiplicity is 1 (since p = p 1). The multiplicity of a prime which does not divide n may be called 0 or may be considered undefined.
A number that does not evenly divide but leaves a remainder is sometimes called an aliquant part of . An integer n > 1 {\displaystyle n>1} whose only proper divisor is 1 is called a prime number . Equivalently, a prime number is a positive integer that has exactly two positive factors: 1 and itself.
6 is the 2nd superior highly composite number, [5] the 2nd colossally abundant number, [6] the 3rd triangular number, [7] the 4th highly composite number, [8] a pronic number, [9] a congruent number, [10] a harmonic divisor number, [11] and a semiprime. [12] 6 is also the first Granville number, or -perfect number.