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Prime Time 1.6 Objective: Write prime factorization using exponents Is it divisible by Only if… 2 The ones digit is divisible by 2 3 5 The sum of the digits is divisible by 3 The last two digits of the # are divisible by 4 It ends in 0 or 5 6 The # is divisible by 2 and 3 9 The sum of the digits is divisible by 9 The # ends in 0 4 10 Did you know? • Did you know that prime means “first or original”? • Did you know that composite means “made up of different parts”? • Did you know that factor means “one thing that influences or contributes to another”? • How do these everyday meanings related to their math meanings? Tell whether each number is prime, composite, or neither • • • • 1) 28 2) 11 3) 1 4) 2 Prime Factorization • Prime Factorization: a composite number expressed as a product of prime numbers. • Factor Trees are often used to help you organize your prime factorization. Example • Find the prime factorizations of the numbers: 54 72 • List the numbers in order from least to greatest • Can you write the answers in exponent form? Powers and Exponents • A product of identical factors can be written using an exponent and a base. Exponent • 32 = 2 x 2 x 2 x 2 x 2 = 2^5 Base Numbers expressed using exponents are called powers. Powers Words 2^5 2 to the fifth power 3^2 3 to the second power or 3 squared 10 to the third power or 10 cubed 7 to the forth power 10 ^ 3 7^4 What about when the exponent is 0 or 1? • If no exponent is given the exponent is considered to be 1. • This does not change the value. • For example: • 5^1=5 • If the exponent is given is 0, the value is one. • (This is 7th grade math) • For example: • 5^0=1 Practice • Write using exponents: • 5x5x5x5= • 6x6x6= • 12 x 12 x 12 x 12 = Practice • Find the prime factorization of the following numbers. Write the final answer using exponents. 8 64 256 Calculator • You can use a calculator to evaluate powers. • To find 3 to the forth power press 3 ^ 4 What is the answer?