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Holt CA Course 1
3-1 Prime Factorization
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson PresentationLesson Presentation
PreviewPreview
Holt CA Course 1
3-1 Prime Factorization
Warm UpWrite each number as a product of two whole numbers in as many ways as possible.
1. 6
2. 16
3. 17
4. 36
1 6, 2 3
1 16, 2 8, 4 4
1 17
1 36, 2 18, 3 12, 4 9, 6 6
Holt CA Course 1
3-1 Prime Factorization
Preparation for Preparation for Number Sense Number Sense (NS2.4)(NS2.4) - Determine the least - Determine the least common multiple and the greatest common multiple and the greatest common divisor of whole numbers;common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form for a fraction).
California Standards
Holt CA Course 1
3-1 Prime Factorization
Objective:Objective: You will learn You will learn how to find the prime how to find the prime factorization of composite factorization of composite numbers.numbers.
Holt CA Course 1
3-1 Prime FactorizationA prime number is a whole number greater than 1 that has exactly two positive factors, 1 and itself. Three is a prime number because its only positive factors are 1 and 3.
A composite number is a whole number that has more than two positive factors. Six is a composite number because it has more than two positive factors—1, 2, 3, and 6. The number 1 has exactly one positive factor and is neither prime nor composite.
Holt CA Course 1
3-1 Prime Factorization
Tell whether each number is prime or composite.
Example 1: Identifying Prime and Composite Numbers
A. 11
11 is prime.
The positive factors of 11 are 1 and 11.
B. 16
16 is composite.
The positive factors of 16 are 1, 2, 4, 8, and 16.
Holt CA Course 1
3-1 Prime Factorization
Tell whether each number is prime or composite.
Check It Out! Example 2
A. 14
14 is composite.
The positive factors of 14 are 1, 2, 7, and 14.
B. 7
7 is prime.
The positive factors of 7 are 1 and 7.
Holt CA Course 1
3-1 Prime FactorizationA composite number can be written as the product of its prime factors. This is called the prime factorization of the number.
You can use a factor tree to find the prime factors of a composite number.
You can also use the “Stairs Method” to find the prime factors of a composite number.
Holt CA Course 1
3-1 Prime Factorization
You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor.
Writing Math
Holt CA Course 1
3-1 Prime Factorization
Write the prime factorization of the number 2424.
Example 3: Using a Factor Tree to Find Prime Factorization
24
8 3
4 2
2 2
The prime factorization of 24 is 2 2 2 3 or 23 3.
Holt CA Course 1
3-1 Prime FactorizationCheck It Out! Example 4
Write the prime factorization of the number 9090.
90
45 2
9 5
3 3
The prime factorization of 90 is 3 3 5 2, or 2 32 5.
Holt CA Course 1
3-1 Prime Factorization
Write the prime factorization of the number 150150.
Example 5: Using a Factor Tree to Find Prime Factorization
150
30 5
10 3
2 5
The prime factorization of 150 is 2 3 5 5, or 2 3 52.
Holt CA Course 1
3-1 Prime FactorizationCheck It Out! Example 6
Write the prime factorization of the number 225225.
225
45 5
9 5
3 3
The prime factorization of 225 is 3 3 5 5, or 32 52.
Holt CA Course 1
3-1 Prime Factorization
You can also use the “Stairs Method” to find the prime factorization of a number. At each step, divide by the smallest possible prime number. Continue dividing until the quotient is 1.
Holt CA Course 1
3-1 Prime Factorization
Write the prime factorization of the number 476476.
Example 7: Using the “Stairs Method” to Find Prime Factorization
476238119
171
22
717
The prime factorization of 476 is 2 2 7 17, or 22 7 17.
Holt CA Course 1
3-1 Prime Factorization
There is only one prime factorization for any given composite number. Example 2A began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result.
476238119
171
22
717
4766834
171
72
217
The prime factorizations are 2 2 7 17 and7 2 2 17, which are the same as 17 2 2 7.
Holt CA Course 1
3-1 Prime Factorization
Write the prime factorization of the number 275275.
Example 8: Using the “Stairs Method” to Find Prime Factorization
27555111
5511
The prime factorization of 275 is 5 5 11, or 52 11.
Holt CA Course 1
3-1 Prime FactorizationCheck It Out! Example 9
Write the prime factorization of the number 324324.
324162
8127
1
22
33
The prime factorization of 324 is 2 2 3 3 3 3, or 22 34.
9333
Holt CA Course 1
3-1 Prime Factorization
Check It Out! Example 10
Write the prime factorization of the number 325325.
32565131
5513
The prime factorization of 325 is 5 5 13, or 52 13.
Holt CA Course 1
3-1 Prime Factorization
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