Prime Factorization of Composite Numbers

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Prime Factorization of Composite Numbers

• By Magan Lantagne

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Definitions

• Prime Number A counting number, greater than
  one, that has exactly two factors, itself and the
  number 1.
• Example- the number 2, whose factors are 1 and 2
• Composite Number A counting number, greater than
  1 that has more than two factors.
• Example- the number 6, whose factors are 1,2,3,
  and 6

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Helpful Hint

• An easy way to remind yourself if a number is
  prime or composite is to remember that composite
  has the word compose in it, and you can make
  composite numbers out of smaller numbers. Just
  like you can compose a piece of music out of
  smaller sounds!

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Definitions Continued

• Prime Factorization When you express a positive
  integer, other than 1, as a product of factors
  that are all prime.
• Basically, what it is, is splitting a composite
  number into smaller numbers that make it up,
  until you cannot split any more numbers
• To view a chart of 100 numbers showing if they
  are either prime or composite visit the following
  link.
• Number Chart

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Now, on to factoring these numbers

• So now that you know what prime factorization
  means, lets take a stab at actually finding the
  prime factorization of composite numbers.
• The easiest way to discover a composite numbers
  factors is by making a Factor Tree.

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The Steps to Making a Factor Tree

• Step 1 Choose a Composite Number
• 36
• Step 2 Find two numbers that can be multiplied
  together to get a product of the composite number
• 6 x 6 36

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Steps Continued

• Step 3 Further breaking down any composite
  numbers
• 6? 2 x 3
• 6? 2 x 3
• Step 4 Gathering all the prime numbers in
  ascending order
• 2 x 2 x 3 x 3
• Step 5 Write out the factors using exponents
• 2² x 3² 36

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The Completed Tree

• 36
• 6 6
• 2 x 3 2 x 3

?
?
?
?
?
?
2² x 3²
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Another Example

• To take a look at another example of factoring a
  number using a factor tree, select the link below
  to see the number 220 be factored out
• http//www.intermath-uga.gatech.edu/dictnary/desc
  ript.asp?termID272

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Extra Practice Worksheet

• Test your knowledge of what youve learned now
  about prime and composite numbers as well as how
  to factor them using a Factor Tree. Worksheet
• Once youve gone through the worksheet, come back
  and link to the answer sheet to find out how well
  you did. Answers

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Works Cited

• MathSteps. 1999. Houghton Mifflin Company. 14,
  April 2004.
• http//www.eduplace.com/math/mathsteps/5/b/
• Bennett, Albert and Nelson, Ted. Mathematics for
  Elementary Teachers. Factors and Multiples. 2001.
  New York, NY.
• Prime Numbers. March 2004.Tampa Palms Elementary
  School.14, April 2004. http//www.sdhc.k12.fl.us/
  tampapalms.elementary/math/topic4/prime.htm
• Intermath. 16, April 2004.
• http//www.intermath-uga.gatech.edu/dictnary/desc
  ript.asp?termID272