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Abundant number

Number Num"ber, n. [OE. nombre, F. nombre, L. numerus; akin to Gr. ? that which is dealt out, fr. ? to deal out, distribute. See Numb, Nomad, and cf. Numerate, Numero, Numerous.] 1. That which admits of being counted or reckoned; a unit, or an aggregate of units; a numerable aggregate or collection of individuals; an assemblage made up of distinct things expressible by figures. 2. A collection of many individuals; a numerous assemblage; a multitude; many. Ladies are always of great use to the party they espouse, and never fail to win over numbers. --Addison. 3. A numeral; a word or character denoting a number; as, to put a number on a door. 4. Numerousness; multitude. Number itself importeth not much in armies where the people are of weak courage. --Bacon. 5. The state or quality of being numerable or countable. Of whom came nations, tribes, people, and kindreds out of number. --2 Esdras iii. 7. 6. Quantity, regarded as made up of an aggregate of separate things. 7. That which is regulated by count; poetic measure, as divisions of time or number of syllables; hence, poetry, verse; -- chiefly used in the plural. I lisped in numbers, for the numbers came. --Pope. 8. (Gram.) The distinction of objects, as one, or more than one (in some languages, as one, or two, or more than two), expressed (usually) by a difference in the form of a word; thus, the singular number and the plural number are the names of the forms of a word indicating the objects denoted or referred to by the word as one, or as more than one. 9. (Math.) The measure of the relation between quantities or things of the same kind; that abstract species of quantity which is capable of being expressed by figures; numerical value. Abstract number, Abundant number, Cardinal number, etc. See under Abstract, Abundant, etc. In numbers, in numbered parts; as, a book published in numbers.

Number Num"ber, n. [OE. nombre, F. nombre, L. numerus; akin to Gr. ? that which is dealt out, fr. ? to deal out, distribute. See Numb, Nomad, and cf. Numerate, Numero, Numerous.] 1. That which admits of being counted or reckoned; a unit, or an aggregate of units; a numerable aggregate or collection of individuals; an assemblage made up of distinct things expressible by figures. 2. A collection of many individuals; a numerous assemblage; a multitude; many. Ladies are always of great use to the party they espouse, and never fail to win over numbers. --Addison. 3. A numeral; a word or character denoting a number; as, to put a number on a door. 4. Numerousness; multitude. Number itself importeth not much in armies where the people are of weak courage. --Bacon. 5. The state or quality of being numerable or countable. Of whom came nations, tribes, people, and kindreds out of number. --2 Esdras iii. 7. 6. Quantity, regarded as made up of an aggregate of separate things. 7. That which is regulated by count; poetic measure, as divisions of time or number of syllables; hence, poetry, verse; -- chiefly used in the plural. I lisped in numbers, for the numbers came. --Pope. 8. (Gram.) The distinction of objects, as one, or more than one (in some languages, as one, or two, or more than two), expressed (usually) by a difference in the form of a word; thus, the singular number and the plural number are the names of the forms of a word indicating the objects denoted or referred to by the word as one, or as more than one. 9. (Math.) The measure of the relation between quantities or things of the same kind; that abstract species of quantity which is capable of being expressed by figures; numerical value. Abstract number, Abundant number, Cardinal number, etc. See under Abstract, Abundant, etc. In numbers, in numbered parts; as, a book published in numbers.

Abundant number

Abundant A*bun"dant, a. [OE. (h)abundant, aboundant, F. abondant, fr. L. abudans, p. pr. of abundare. See Abound.] Fully sufficient; plentiful; in copious supply; -- followed by in, rarely by with. ``Abundant in goodness and truth.' --Exod. xxxiv. 6. Abundant number (Math.), a number, the sum of whose aliquot parts exceeds the number itself. Thus, 1, 2, 3, 4, 6, the aliquot parts of 12, make the number 16. This is opposed to a deficient number, as 14, whose aliquot parts are 1, 2, 7, the sum of which is 10; and to a perfect number, which is equal to the sum of its aliquot parts, as 6, whose aliquot parts are 1, 2., 3. Syn: Ample; plentiful; copious; plenteous; exuberant; overflowing; rich; teeming; profuse; bountiful; liberal. See Ample.

Abundant A*bun"dant, a. [OE. (h)abundant, aboundant, F. abondant, fr. L. abudans, p. pr. of abundare. See Abound.] Fully sufficient; plentiful; in copious supply; -- followed by in, rarely by with. ``Abundant in goodness and truth.' --Exod. xxxiv. 6. Abundant number (Math.), a number, the sum of whose aliquot parts exceeds the number itself. Thus, 1, 2, 3, 4, 6, the aliquot parts of 12, make the number 16. This is opposed to a deficient number, as 14, whose aliquot parts are 1, 2, 7, the sum of which is 10; and to a perfect number, which is equal to the sum of its aliquot parts, as 6, whose aliquot parts are 1, 2., 3. Syn: Ample; plentiful; copious; plenteous; exuberant; overflowing; rich; teeming; profuse; bountiful; liberal. See Ample.

- 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...

- In mathematics, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in a particular, rigorous sense, has many divisors...

- In mathematics, a highly abundant number is a natural number with the property that the sum of its divisors (including itself) is greater than the sum...

- primitive abundant number is an abundant number whose proper divisors are all deficient numbers. For example, 20 is a primitive abundant number because:...

- A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater...

- number 1,421,280 – harmonic divisor number 1,441,440 – colossally abundant number, superior highly composite number 1,441,889 – Markov number 1,539,720...

- following 599 and preceding 601. Six hundred is a composite number, an abundant number, a pronic number and a Harshad number. In the United States, a credit...

- base 9 232,792,560 – superior highly composite number; colossally abundant number; the smallest number divisible by all the numbers 1 through 22 244...

- factorial of 9, smallest odd abundant number (divisors less than itself add up to 975); smallest odd primitive abundant number; smallest odd primitive semiperfect...

- member of the (22)q family in this form. 20 is the smallest primitive abundant number. An icosahedron has 20 faces. A dodecahedron has 20 vertices. 20 can...

- In mathematics, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in a particular, rigorous sense, has many divisors...

- In mathematics, a highly abundant number is a natural number with the property that the sum of its divisors (including itself) is greater than the sum...

- primitive abundant number is an abundant number whose proper divisors are all deficient numbers. For example, 20 is a primitive abundant number because:...

- A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater...

- number 1,421,280 – harmonic divisor number 1,441,440 – colossally abundant number, superior highly composite number 1,441,889 – Markov number 1,539,720...

- following 599 and preceding 601. Six hundred is a composite number, an abundant number, a pronic number and a Harshad number. In the United States, a credit...

- base 9 232,792,560 – superior highly composite number; colossally abundant number; the smallest number divisible by all the numbers 1 through 22 244...

- factorial of 9, smallest odd abundant number (divisors less than itself add up to 975); smallest odd primitive abundant number; smallest odd primitive semiperfect...

- member of the (22)q family in this form. 20 is the smallest primitive abundant number. An icosahedron has 20 faces. A dodecahedron has 20 vertices. 20 can...

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