# 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

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### 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 ...

### The Penguin Dictionary of Curious and Interesting Numbers (1997)

by David Wells

The numbers of spheres that can touch one sphere in higher dimensions up to
dimension 9 are: Abundant numbers 12 is **the first abundant number**, meaning
that it is less than the sum of its factors excluding itself: 1 + 2 + 3 + 4 + 6 = 16.

### 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 ...

### Encyclopaedia Britannica; Or A Dictionary of Arts, Sciences, and Miscellaneous Literature (1823)

IMPERFEct Number, is that whose aliquot parts, taken all together, do not make a
sum that is equal to the number itself, but either exceed it, or fall short of it; **being
an abundant number** in the former case, and a defective number in the latter.

### Dictionary of Phrase and Fable (1900)

Giving the Derivation, Source, Or Origin of Common Phrases, Allusions, and Words that Have a Tale to Tell by Ebenezer Cobham Brewer

**Abundant Number** (An}. A number
such that the «um of all its divisors (except itself) is greater than the number itself.

### Encyclopaedia of the History of Science, Technology, and Medicine in Non-Westen Cultures (2013)

by Helaine Selin

every even-times-even number has factors less than itself, • the first abundant
number is 12, and the first odd one in this class is 945; and • if 2" S is a perfect
number, then 2" S is **an abundant number**, and 2" S is a deficient number.

### Encyclopaedia Perthensis, Or, Universal Dictionary of the Arts, Sciences, Literature, Etc (1816)

Intended to Supersede the Use of Other Books of Reference

**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 are, 1, 2, and 7
, which make no more than 10: and to a perfä number, or one to which its aliquot
...

### 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, for the sum of its aliquot parts (1 + 2 + 3 + 4 +6) is 16. It is thus
distinguished ...

### The Encyclopedia of Eastern Orthodox Christianity, 2 Volume Set (2010)

by John Anthony McGuckin

The church is renowned for sending out **an abundant number** of priests
to ...

### Encyclopaedia Metropolitana: Miscellaneous and lexicographical (1845)

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 ...

### Encyclopædia metropolitana; or, Universal dictionary of knowledge, ed. by E. Smedley, Hugh J. Rose and Henry J. Rose. [With] Plates (1845)

by Edward Smedley

**ABUNDANT number**, a number, the sum of whose aliquot parts exceeds the
number itsejf. Thus 18 is **an abundant number** because 1, 2, 3, 6, and 9, its
aliquot parts, are 31, 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 Mathematics Dictionary (1992)

by R.C. James, Glenn James

**abundant number**. See NUMBER — perfect number. Acceleration
Accumulation AC-CEL'ER-A'TION, n. The time rate of change of.

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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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