Home
Math symbols
Jokes
Forum
About us
Links
Contact us
Site map
Search The Site
   
   Program of Lessons
 
 Study Guide
 Topics of problems
 Tests & exams
www.bymath.com Study Guide - Arithmetic Study Guide - Algebra Study Guide - Geometry Study Guide - Trigonometry Study Guide - Functions & Graphs Study Guide - Principles of AnalysisStudy Guide - Sets Study Guide - Probability Study Guide - Analytic Geometry Select topic of problems Select test & exam

Factorization. Resolution into prime factors


Prime factoring of composite numbers.

Any composite number can be presented as a product of  prime factors by the single way. For example,

48 = 2 ∑ 2 ∑ 2 ∑ 2 ∑ 3,   225 = 3 ∑ 3 ∑ 5 ∑ 5,  1050 = 2 ∑ 3 ∑ 5 ∑ 5 ∑ 7.

For small numbers this operation is easy. For large numbers it is possible to use the following way. Consider the number 1463. Look over prime numbers one after another from the table:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,

47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,

103, 107, 109, 113, 127, 131, 137, 139, 149, 151,

157, 163, 167, 173, 179, 181, 191, 193, 197, 199

and stop, if the number is a factor of 1463. According to the section the divisibility criteria, we see that numbers 2, 3 and 5 arenít factors of 1463. But this number is divisible by 7, really, 1463 : 7 = 209. By the same way we test the number 209 and find its factor:  209 : 11 = 19. The last number is a prime one, so the found prime factors of  1463 are: 7, 11 and 19,  i.e. 1463 = 7 ∑ 11 ∑ 19.  It is possible to write this process using the following record:

Number          Factor
----------------------------
1463                  7
  209                11
   19                 19
----------------------------

Back


| Home | About us | Links | Contact us |

Copyright © 2002-2007 Dr. Yury Berengard. All rights reserved.