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4-2 6th grade math Prime Factorization Objective • To use divisibility rules to check for divisibility and write the prime factorization of numbers in exponential form. • Why? To help you with prime factoring, simplifying fractions, division. California State Standards NS 1.4 (Gr. 5): Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show the multiples (e.g., 24 = 2 x 2 x 2 x 3 = 2³ x 3) MR 3.3: Develop generalizations of the results obtained and the strategies used and apply them in new problem situations. Vocabulary • Divisible – A number is divisible by another number if the remainder is zero after dividing. • 36 ÷ 6 = 6 • Prime Number – A whole number greater than one with only two factorsitself and one. • 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 57, 59, … • Composite Number – A whole number greater than one that has more than two factors • 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, … • Prime Factorization – Writing a number as the product of its prime factors • 24 = 2 x 2 x 2 x 3 Divisibility Rules! Divisibility Rules A number is divisible by: 2 If the last digit ends in 0, 2, 4, 6, 8 (any even number) 3 If the sums of the digits is divisible by 3 (may be even or odd) 4 If the last two digits are divisible by 4 (only an even number) 5 If the last digit ends in 0 or 5 (any number ending in 5 or 0) 6 If the number is divisible by 2 and 3 (only an even number) 9 If the sum of the digits is divisible by 9 (may be even or odd) 10 If the last digit ends with a 0 (only ends in 0) How To Prime Factor - #1 • Make a ‘Factor Tree’ 40 2 x 20 5x4 2x2 = 2³ x 5 Factor out each number until you get only primes Circle the prime numbers to be organized Put final answer in exponential form How to Prime Factor- #2 Make a ‘Factor Ladder’ Put the number at the top of a ‘ladder’= box If it is even, begin ÷ 2 If not, try greater primes like 3, 5, 7, 9 Only move on when the current number you are using doesn’t work anymore Use the divisibility rules to help The numbers on the side of the ladder are the numbers used for prime factorization. prime factor 40 40 2 20 2 10 2 5 = 2³ x 5 Try It! Tell if each number is divisible by: 2, 3, 4, 5, 6, 9,or 10 1) 3,742 2) 5,310 3) 47,388 4) 9,999 5) 41, 112 1) 2 2) 2, 3, 5, 6, 9, 10 3) 2, 3, 4, 6 4) 3, 9 5) 2, 3, 4, 6, 9 Try Some More! 1) 64 Use exponents to write the prime factorization of each number. 1) 64 2) 48 3) 76 2 32 2 16 2 8 2 4 2 2 64 = 2⁶ 2) 3) 76 2 38 2 19 76 = 2² x 19 48 2 24 2 12 2 6 2 3 48 = 2⁴ x 3 More to Try Prime factor using exponents. 9) 9) 81 81 9 9 3x3 3x3 81 = 3⁴ 10) 90 10) 90 9 10 3x3 5x2 90 = 2 x 3² x 5 Objective Review • To use divisibility rules to check for divisibility and write the prime factorization of numbers in exponential form. • Why? You can now prime factor efficiently, simplify fractions, and divide better Independent Practice • Complete problems 1223 • Copy original problem first. • Show all work! • If time, complete Mixed Review: 24-29 • If still more time, work on Accelerated Math.