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.