# 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 Micron Millenia P5 - 133 MHz with 32 MB RAM, Windows 95 OS.