Abundant number is a mathematical term that is used to describe a type of number that has a special property. It is a number that is greater than the sum of its proper divisors. In other words, when you add up all the factors of a number except for the number itself, the result is less than the number itself. This article will explore the definition and meaning of abundant number, as well as its origins and associations.
Definitions
An abundant number is a positive integer that is greater than the sum of its proper divisors. For example, the number 12 is an abundant number because its proper divisors are 1, 2, 3, 4, and 6, and their sum is 16, which is greater than 12.
Origin
The concept of abundant numbers dates back to ancient times, with Greek mathematicians such as Nicomachus and Euclid studying the properties of these numbers. The term “abundant number” was first used in the 17th century by the French mathematician Étienne Pascal.
Meaning in different dictionaries
In the Oxford English Dictionary, an abundant number is defined as “a number that is greater than the sum of its proper divisors.” Merriam-Webster defines it as “a number that exceeds the sum of its proper divisors.”
Associations
Abundant numbers are closely related to other types of numbers, such as perfect numbers and deficient numbers. A perfect number is a number that is equal to the sum of its proper divisors, while a deficient number is a number that is less than the sum of its proper divisors.
Synonyms
There are several synonyms for abundant number, including excessive number, superabundant number, and superfluous number.
Antonyms
The antonyms of abundant number are deficient number and perfect number.
The same root words
The root word of abundant is “abound,” which means to be plentiful or abundant. This is reflected in the meaning of abundant number, which is a number that is greater than the sum of its proper divisors.
Example Sentences
Here are some example sentences that use the term abundant number:
- The number 18 is an abundant number because its proper divisors are 1, 2, 3, 6, and 9, and their sum is 21, which is greater than 18.
- Mathematicians have been studying abundant numbers for centuries, and they continue to uncover new properties and relationships.
- Abundant numbers are important in number theory, and they have applications in cryptography and other areas of computer science.