PERFECT NUMBER Meaning and
Definition
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A perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself). In other words, it is a number whose proper divisors add up to the number itself.
To understand this definition more clearly, let's break it down. A positive integer is any whole number greater than zero. The proper divisors of a number are the positive divisors (factors) of the number, excluding the number itself. For example, the proper divisors of the number 6 are 1, 2, and 3.
A perfect number occurs when the sum of its proper divisors equals the number itself. For instance, the proper divisors of the number 6 (1, 2, and 3) add up to 6, making it a perfect number.
Perfect numbers have been studied since ancient times and have fascinated mathematicians for centuries. The ancient Greeks were the first to explore these numbers, and Euclid mentioned them in his famous Elements. As of now, only a few perfect numbers have been discovered, the first four being 6, 28, 496, and 8128. The largest perfect number found to date is 2^82,589,933 − 1, a number with over 24 million digits.
Perfect numbers have connections to various fields of mathematics, such as number theory and algebra. Their properties have been extensively researched, leading to many interesting theorems and conjectures in the mathematical world.
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In arith., a number equal to the sum of all its divisions; to perfection, in the highest degree of excellence.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
Common Misspellings for PERFECT NUMBER
- oerfect number
- lerfect number
- -erfect number
- 0erfect number
- pwrfect number
- psrfect number
- pdrfect number
- prrfect number
- p4rfect number
- p3rfect number
- peefect number
- pedfect number
- peffect number
- petfect number
- pe5fect number
- pe4fect number
- perdect number
- percect number
- pervect number
- pergect number
Etymology of PERFECT NUMBER
The term "perfect number" has its roots in Greek and Latin. The Greek term is "teleios" (τέλειος), meaning "complete" or "perfect". The Latin equivalent is "perfectus", also meaning "perfect" or "finished". The word "perfect" in this context refers to a number that is equal to the sum of its proper divisors, excluding the number itself. The concept of perfect numbers dates back to ancient Greek mathematicians, with Euclid being one of the first known mathematicians to study and define perfect numbers.
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