# Fibonacci Factorization

#### Finding the factors of the Fibonacci numbers

##### Objective

The students will practice prime factorizations using Fibonacci numbers. This is only a
rough outline of the material. During the factor search I found the students tended to
quit checking for factors after 7 or 11. This led to a discussion of whether factors could
be larger than 11. This then led to questions of how far one has to go to have exhausted a
search for factors.

Find the prime factorizations of the following numbers:

1 ____________________________

1 ____________________________

2 ____________________________

3 ____________________________

5 ____________________________

8 ____________________________

13 ____________________________

21 ____________________________

34 ____________________________

55 ____________________________

89 ____________________________

144 ____________________________

233 ____________________________

377 ____________________________

610 ____________________________

987 ____________________________

1597 ____________________________

2584 ____________________________

4181 ____________________________

6765 ____________________________

10946 ____________________________

Do any two consecutive numbers have common factors (the same factor appears in two
consecutive factorizations)? _________

Which number have consecutive common factors?

[Note that 4181 is particularly slippery: it has factors of 37*113. Do not reveal
this to the students. 17711, another Fibonacci number, has factors to 89*199.]

*Developed by Dana Lee Ling with the support and funding of a U.S. Department of
Education Title III grant and the support of the College of Micronesia - FSM. Notebook
material ©1999 College of Micronesia - FSM. For further information on this project,
contact dleeling@comfsm.fm Designed and run on
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