Definitions for practical number
prac·ti·cal num·ber

WiktionaryRate this definition:0.0 / 0 votes

1. practical numbernoun

   Any positive integer having the property that all smaller integers can be represented as sums of distinct divisors of it

WikipediaRate this definition:0.0 / 0 votes

1. Practical number

   In number theory, a practical number or panarithmic number is a positive integer n {\displaystyle n} such that all smaller positive integers can be represented as sums of distinct divisors of n {\displaystyle n} . For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well as these divisors themselves, we have 5 = 3 + 2, 7 = 6 + 1, 8 = 6 + 2, 9 = 6 + 3, 10 = 6 + 3 + 1, and 11 = 6 + 3 + 2. The sequence of practical numbers (sequence A005153 in the OEIS) begins Practical numbers were used by Fibonacci in his Liber Abaci (1202) in connection with the problem of representing rational numbers as Egyptian fractions. Fibonacci does not formally define practical numbers, but he gives a table of Egyptian fraction expansions for fractions with practical denominators.The name "practical number" is due to Srinivasan (1948). He noted that "the subdivisions of money, weights, and measures involve numbers like 4, 12, 16, 20 and 28 which are usually supposed to be so inconvenient as to deserve replacement by powers of 10." His partial classification of these numbers was completed by Stewart (1954) and Sierpiński (1955). This characterization makes it possible to determine whether a number is practical by examining its prime factorization. Every even perfect number and every power of two is also a practical number. Practical numbers have also been shown to be analogous with prime numbers in many of their properties.

WikidataRate this definition:3.0 / 1 vote

1. Practical number

   In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well as these divisors themselves, we have 5=3+2, 7=6+1, 8=6+2, 9=6+3, 10=6+3+1, and 11=6+3+2. The sequence of practical numbers begins Practical numbers were used by Fibonacci in his Liber Abaci in connection with the problem of representing rational numbers as Egyptian fractions. Fibonacci does not formally define practical numbers, but he gives a table of Egyptian fraction expansions for fractions with practical denominators. The name "practical number" is due to Srinivasan, who first attempted a classification of these numbers that was completed by Stewart and Sierpiński. This characterization makes it possible to determine whether a number is practical by examining its prime factorization. Any even perfect number and any power of two is also a practical number. Practical numbers have also been shown to be analogous with prime numbers in many of their properties.

How to pronounce practical number?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say practical number in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of practical number in Chaldean Numerology is: 5

2. Pythagorean Numerology

   The numerical value of practical number in Pythagorean Numerology is: 3

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Practical_Number
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Practical_Number
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=practical number