50 Part 1: The World of Numbers
CHECK POINT
Decide if each number is prime or composite. If it’s composite, give a pair of factors
other than the number and 1.- 51
- 91
- 173
4. 229
5. 5,229
Prime Factorization ...................................................................................................................
Factoring is the process of starting with the product and finding the factors that produced it.
(Factoring is related to division, but not quite the same.) You could factor 24 by writing it as
2 v 12, or 3 v 8, or 2 v 3 v 4, and other possibilities.
A number can have lots of different factorizations, but it has only one prime factorization. A prime
factorization expresses the number as a product of only prime numbers. The prime factorization
of 24 is 2 v 2 v 2 v 3.DEFINITION
The prime factorization of a number is a multiplication that uses only prime numbers
and produces the original number as its product.You can find the prime factorization just by finding primes that are factors of the number by
trial and error, but having a way to organize the search does make things faster. One method for
finding the prime factorization of a number is called a factor tree.Factor Trees
A factor tree is a device that allows you to start with any two factors of a number and to work in an
organized fashion to the prime factorization.DEFINITION
A factor tree is a method of finding the prime factorization of a number by starting
with a pair of factors and then factoring each of those numbers, continuing until no
possible factoring remains.