Download Focus Question: How many unique prime factorizations of a number

May 02, 2015
Focus Question: How many unique prime
factorizations of a number are there?
Read the introduction on page 46 in your
book.
May 02, 2015
What do exponents do?
They give us the power to write the product of
repeated factors.
Yesterday we found the longest string of
factors for 840. How could we communicate
our method to someone else?
We decomposed numbers into longer and longer strings of
factors until we found the longest string, which turned out
to be made up of all prime numbers.
May 02, 2015
Vocabulary:
exponent-tells you how many times to multiply a
number by itself
May 02, 2015
Exponent Video
Write the following without exponents:
33 x 72 x 11.
3 x 3 x 3 x 7 x7 x 11
What does it equal?
14,553
May 02, 2015
81 can be written as 9 x 9 or 92. This means
that 9 is used as a factor twice. 81 can also be
written as 3 x 3 x 3 x 3 or 34. This means that 3
is used as a factor four times. Which
factorization is the prime factorization?
3 x 3 x 3 x 3 or 34
May 02, 2015
Write the prime factorization of 18 using
exponents.
2 x 32
May 02, 2015
2,500 can be written as 50 x 50 or 502. 2,500
can also be written as 2 x 2 x 5 x 5 x 5 x5 or
22 x 54. How many times is 50 used as a factor
in 502?
twice
May 02, 2015
How many times is 5 used as a factor in
22 x 54? How many times is 2 used?
5 is used four times and 2 is used twice.
Which factorization of 2,500 is the prime
factorization?
2 x 2 x 5 x 5 x 5 x 5 or 22 x 54
May 02, 2015
In the Problem today you will continue to find
the prime factorization of a number and use it
to answer the questions about the number.
Complete the problem on page 47. Be sure to
label the top of your paper as Problem 3.2.
Also be sure to label the sections with the
correct letters and the questions with the
correct numbers.
Let's complete Section A then stop. We will go
over it then you can complete the rest of the
page.
May 02, 2015
For Question A, part 1: did everyone in your
group get the same prime factorization for 36?
These are some questions you should ask
yourself as you determine prime factorizations:
• Are all the numbers in your string prime?
• Did you keep track of all the prime factors as
you found them?
• Did you multiply your string of numbers to
check that the product was 36?
• Remember, order does not matter.
May 02, 2015
Complete the rest of the problem. We will
check it when everyone is finished.
How can we rewrite the prime factorization of
36 using exponents?
22 x 32
Do we all need to use the same strategy to find
the prime factorization of a number?
May 02, 2015
Name a nonprime factor of 36. What is the
prime factorization of that factor?
How can you tell whether a number is prime or
composite by looking at its prime factorization?
Give an example.
If a number is prime, it has only one factor,
itself, in its prime factorization.
May 02, 2015
How can you tell whether a number is even or
odd by looking at its prim factorization? Give an
example?
If there is a factor of 2 in the prime factorization,
the number is even. Otherwise, it is odd.
Find the prime factorization of 120.
23 x 3 x 5
May 02, 2015
What do you multiply 5 x 23 by to get 120?
3
Is 23 x 7 a factor 120? Explain.
No because 7 is not in the prime factorization
of 120.
Is 23 x 32 x 5 a multiple of 120? Use the prime
factorization of 120 to justify your reasoning.
yes; the prime factorization of 120 is included in
the number 23 x 32 x 5.
May 02, 2015
ACE: Page 54
Questions 5-20; 31-35