# Abundant number

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## Definition of the noun Abundant number

What does Abundant number mean as a name of something?

**noun**

- [
*number theory*] A number that is less than the sum of all of its divisors except itself.- synonym: excessive number

## Explanation

**Abundant number**: In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example.

- also known as 过剩数

## Printed dictionaries and other books with definitions for Abundant number

Click on a title to look inside that book (if available):

### The Kingdom of Infinite Number (2001)

A Field Guide by Bryan Bunch

FIELD MARKS * An abundant number is a whole number for which the sum of its
divisors, not including the number itself, is greater than the number*.

**The lowest abundant number**is 12, since its proper divisors (excluding itself) are 1, 2, 3, 4, and ...

### How to Think About Analysis (2014)

by Lara Alcock

Definition: * An abundant number is a positive integer n whose divisors add up to
more than* .

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

See also ABUNDANCE, **ABUNDANT NUMBER** References Guy, R. K. "The
Second Strong Law of Small Numbers." Math. Mag. 63, 3Á/0, 1990. Abundant
Number * An abundant number is an INTEGER n which is not a PERFECT
NUMBER and* ...

### The Mathematics of Egypt, Mesopotamia, China, India, and Islam (2007)

A Sourcebook by Victor J. Katz, Annette Imhausen

The two kinds related to the perfect number are **the
abundant number** and the deficient number. * The abundant number is a number
such* ...

### Math Dictionary for Kids (2006)

The Essential Guide to Math Terms, Strategies, and Tables by Theresa R. Fitzgerald

Example: |+3| = 3 and |-3| = 3 **Abundant Number**
A ...

### Encyclopaedia Londinensis, or, Universal dictionary of arts, sciences, and literature (1810)

by John Wilkes (of Milland House, Sussex)

**Abundant Number**, in arithmetic, is a number, the sum of whose aliquot parts is
greater than the number itself.

**An abundant number** is opposed to a deficient
number, or that w hich is greater than all its aliquot parts taken together; as 14, ...

### Mathematics Illustrated Dictionary (2003)

Facts, Figures, and People by Jeanne Bendick

absolute value 15 **abundant number** or excessive number Larger measures use
the mks (meter, kilogram, and second) system. absolute value. The absolute
value of a number, whether it is positive or negative, is always positive. For
example ...

### The Century Dictionary and Cyclopedia: The Century dictionary ... prepared under the superintendence of William Dwight Whitney ... rev. & enl. under the superintendence of Benjamin E. Smith (1911)

—**Abundant number**, in arith., a number the
sum of whose aliquot parts exceeds the number itself. Thus, 12 is an abundant
number, ...

### Encyclopaedia Metropolitana, Or, Universal Dictionary of Knowledge (1845)

Comprising the Twofold Advantage of a Philosophical and an Alphabetical Arrangement, with Appropriate Engravings by Edward Smedley, Hugh James Rose, Henry John Rose

**ABUNDANT number**, a number, the sum of whose aliquot parts exceeds the
number itself. Thus 18 is **an abundant number** because 1, 2, 3, 6, and 9, its
aliquot parts, are 21, or greater than that number. When the aliquot parts of any
number ...

### Encyclopaedia Metropolitana; Or, Universal Dictionary of Knowledge on an Original Plan Comprising the Twofold Advantage of a Philosophical and an Alphabetical Arrangement, with Appropriate Engravings Edited by Edward Smedley, Hugh James Rose, Henry John Rose (1845)

Miscellaneous and lexicographical, vol. 1

Thus l8 is **an Abundant Number**, because 1, 2, 3, 6. and 9, its
aliquot parts, are 21, or greater than that number. When the aliquot parts of any
number are ...

### The Century dictionary and cyclopedia (1906)

a work of universal reference in all departments of knowledge with a new atlas of the world by William Dwight Whitney, Benjamin Eli Smith

—**Abundant number**. See abundant — Algebraic number, a root of an algebraic
equation with whole numbers for its coefficients.— Alternate, amicable,
apocalyptic, appllcate, artificial numbers. See the adjectives. — A number of,
several; ...

### The Century dictionary (1906)

Seedcjinition— **Abundant number**, in arith., a number the sum of whose aliquot
parts exceeds the number itself. Thus, 12 is **an abundant number**, for the sum of
its ...

### The new encyclopædia; or, Universal dictionary ofarts and sciences (1807)

by Encyclopaedia Perthensis

**An abundant number** is opposed to a deficient number, or that which is greater
than all its aliquot parts taken together; as 14, whose aliquot parts <pe, 1, z, and 7
, which make no more than jo: and to a perse fl number, or one to which its
aliquot ...

## Online dictionaries and encyclopedias with entries for Abundant number

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## Video about Abundant number

**Abundant number Meaning**

Video shows what abundant number means. A number that is less than the sum of all of its divisors except itself.. abundant number synonyms: excessive ...

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