Warm UPStep 1: Write the whole numbers from 2 through 48. Step 2: Circle 2 and cross out all multiples of 2 other than 2 (the first row below is shown for you)Step 3: Then go to the next remaining number after 2, circle it, and cross out all its multiples other than itself.Step4: Repeat until every number is either circled or crossed out.

Prime and Composite Numbers

• A prime number is a number greater than 1 whose only whole number factors are and itself.

• A composite number is a whole number greater than 1 that has whole number other than 1 and itself.

• The number is neither prime nor composite.

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factors

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Writing Factors of a Number• Field Trip: A class of 36 students is on a field trip at the

aquarium. The teacher wants to break the class into groups of the same size. • Find all possible group sizes by writing all of

the of 36:factors

Identifying Prime and Composite Numbers

Ex: Tell whether the number is prime or composite:1. 56

2. 11

List the Factors:56 = 1 x 56 = 2 x 28 = 4 x 14 = 7 x 8

List the Factors:11 = 1 x 11

Prime Factorization & Factor Trees

• Prime Factorization: to factor a whole number as a of prime numbers.• You can use a tree. • Use an when a prime number factor appears

more than once.Ex: Use a factor tree to write the prime factorization of 54:

productfactor

exponent

Both factors trees = 2 x 3 x 3 x 3 = 2 x 33

Greatest Common Factor (GCF)• Common Factor : a whole number that is a factor of

two or more whole numbers• Greatest Common Factor (GCF): the of

the common factors, which can be found two ways:

1. Making a list of all factors: Ex: Find the GCF of 48, 24, and 36:

nonzero

greatest

Greatest Common Factor (GCF)2. Use prime factorization: Ex: Find the GCF of 180 & 126

Guided Practice1. Write all the factors of the number and tell whether it is prime or composite:a) 35 b) 65 c) 47

2. Use a factor tree to write the prime factorization of the number: 48

3. Find the GCF of 16 and 28 by listing the factors:

4. Find the GCF of 90 and 150 by using prime factorization

1, 5, 7, 35; Composite 1, 5, 13, 65; Composite 1, 47; Prime

24 x 3

16: 1, 2, 4, 8, 1628: 1, 2, 4, 7, 14, 28The GCF is 4

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