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Monomials and Factoring Honors Math – Grade 8

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KEY CONCEPT Prime and Composite Numbers A whole number, greater than 1, for which the only factors are 1 and itself is called a prime number. A whole number, greater than 1, that has more than two factors is called a composite number. Examples: 2, 3, 4, 5, 11, 13, 17, 19 Examples: 4, 6, 8, 9, 10, 12, 14, 15, 200 0 and 1 are NEITHER prime nor composite.

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Find the prime factorization of 90 Make a factor tree What are some factors of 90 that are not prime? Recall: factors are numbers multiplied to obtain a product. Are 9 and 10 prime? Write factors for each number that is composite. Circle the prime numbers. A whole number expressed as the product of prime numbers is called the prime factorization of the number.

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Factor the monomial completely A monomial is in factored form when it is expressed as the product of prime numbers and variables, and no variable has an exponent greater than 1. -12 = -1 x 12 Write the prime factorization of 12. 12 = 2 x 2 x 3 Write the exponents in expanded form.

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Find the GCF of 48 and 60 Write the prime factorization of each number. “Factor” each number. Circle the common prime factors. The common prime factors are 2, 2, and 3. The product of the common prime factors is called the greatest common factor (GCF). The GCF of 48 and 60 = 2 x 2 x 3 = 12

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KEY CONCEPT Greatest Common Factor (GCF) The GCF of two or more monomials is the product of their common factors when each monomial is written in factored form. If two or more integers or monomials have a GCF of 1, then the integers or monomials are said to be relatively prime.

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Find the GCF & Circle the common prime factors. Factor each number. The GCF is the product of common prime factors.

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Find the GCF & Circle the common prime factors. Factor each number. The GCF is the product of common prime factors.

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GCF Circle the common prime factors. Factor each number. The GCF is the product of common prime factors.

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