Download 3. Prime Fatorization - Livingston Public Schools

3. Prime Fatorization
Warm Up 10/5/15
October 05, 2015
SOLUTIONS:
Work with your partner. Prime Factorization
Without dividing, how can you tell when a number is divisible by another number?
1. Highlight all the numbers that are divisible by 2.
2. Put a box around the numbers that are divisible by 3.
3. Underline the numbers that are divisible by 5.
4. Circle all the numbers that are divisible by 10.
What patterns do you notice? How can we determine when a number is divisible by 2, 3, 5, and 10?
You will now use your knowledge of divisibility rules to help you write the prime factorization of numbers.
Prime Factorization: the way to represent any natural number as the product of only prime numbers...
We use "subsequent division" to factor out the prime factors. Start by dividing by the lowest possible prime number, and then by the next lowest, and so on.
In our school we call this "monkey division" because the result looks like monkey bars. We must recall our prime numbers in order to do this process...
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97... 3. Prime Fatorization
October 05, 2015
Find the prime factorization of 12 using subsequent division. (I want to know what prime factors make 12)
1. Divide by the smallest prime number with no remainder.
2. Continue this process until your
final number is 1 (one).
2 12
2 6
3 3
1
3. The numbers left on the outside
are the factors that multiply to make 12.
Find the prime factorization of 240 using subsequent division. (I want to know what prime factors make 480)
2
1. Divide by the smallest prime number with no remainder.
240
2. Continue this process until your
final number is 1 (one).
3. The numbers left on the outside
are the factors that multiply to make 240.
2 2 3 is the prime factorization of 12
We write our solution in exponential form 22 3
________ is the prime factorization of 480
We write our solution in exponential form ________
Find the number represented by the prime factorization...
Find the number represented by the prime factorization...
22 3 5
32 5
Practice: a. b.
264 225
c.
333
2
a. b.
3 225
264 2 132
66
2
75
3
3
33
11
11
1
c.
333
3
3
5
25
5
5
1
37
111
37
1
3. Prime Fatorization
October 05, 2015