Before doing this activity. . .

• you should review prime numbers, prime factors, prime factorization, and exponents.
• print a copy of the recording sheet.

ACTIVITY:

1.	To find the prime factorization of a number, enter the number as the numerator and the denominator of a fraction.  (You are entering the number as a fraction to take advantage of the  key on the TI-73.  The  key simplifies the fraction one factor at at time.) For example, to find the prime factorization of 24:  Type 24, press  , type 24, and press  .
2.	The arrow next to the fraction means that the fraction can be simplified.  Press  ,  .  The calculator will display the new fraction simplified by the lowest prime factor.  Record this factor on the recording sheet under Prime Factors.
3.	Repeat the  ,  , record process until the fraction has been simplified completely.  (Remember that when the calculator displays 24/24 Simp Fac=2 12/12 this means:  24/24 divided by 2/2 equals 12/12.) The product of the common prime factors is the prime factorization of the number.  Since the prime factors of 24 are 2, 2, 2, and 3, its prime factorization can be written as 2 x 2 x 2 x 3.  Record this on the recording sheet under Prime Factorization.  The prime factorization can also be written in a shorter way by using exponents, 23 x 3.  (Note that 3 can be written as 31.)  Record this on the recording sheet under Prime Factorization (use exponents).
	Notice that if you were to press  ,  one last time, that the last common factor would be 1.  Does this always happen?  Why?  Yes, this always happens because 1 is always a common factor for any pair of numbers.  In that case, then why do we not record 1 as a prime factor?  The reason you may recall is because 1 is not a prime number, in fact, 1 is neither prime nor composite.
4.	Repeat steps 1 through 3 with the remaining numbers on the recording sheet.

LOOKING BACK:
This activity used the TI-73 calculator's ability to simplify fractions to find the prime factorization of a number.  Your students could utilize the technique demonstrated in this activity anytime they need to find the prime factorization of a number.

QUESTIONS:
After completing this activity, prepare your responses to the following questions.

1. Explain the process the calculator is using to help you find the prime factorization of a number?
2. What is the prime factorization of the number 720?
3. Given a number and a prime factorization, explain how you could prove that this is the prime factorization of the given number?
4. Is 2^3 x 3^2 and 3^3 x 2^2 the prime factorization of the same number? Explain why or why not.  (Note:  2^3 means 2 is the base and 3 is the exponent.)