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Review A prime number is a whole number with only two factors, itself and 1. Ex. 2,3,5,7,11,13,17,19,23,29,31,... A composite number is a whole number greater than 1 that is not a prime number.

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A prime factor is a prime number that is a factor of a number. Find the factors of 24 The prime factors of 24 are:

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The prime factorization of a natural number is the number written as a product of its prime factors. The prime factorization of 24 is :

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Write the prime factorization for 92400 This could take a while. Especially without a calculator. It would be useful if we had some way of quickly determining which numbers divide into 92400. The following divisibility rules could reduce the amount of trial and error when finding factors.

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2 : The number is even 3 : The sum of the digits is a multiple of 3 4 : The last 2 digits are divisible by 4 5 : The number ends in 5 or 0 6 : The number is divisible by 2 and 3 8 : The last 3 digits are divisible by 8 9 : The sum of the digits is a multiple of 9 10 : The number ends in 0 100: The number ends in 00

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11 If you sum every second digit and then subtract all other digits and the answer is zero EXAMPLE: See whether the following numbers are is divisible by 11 132 1331 365167484

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7 Remove the last digit of the number, double it, and then subtract it from the rest of the number (not including that last digit which was removed). If you get a number divisible by 7, then your original number is divisible by 7

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For example: 273: Take the last digit 3, double it to get 6, and then subtract it from 27: 27 – 6 = 21. Pretty wild, huh? Who figures this stuff out, anyway? EXAMPLE: See whether the following numbers are is divisible by 7 371 251 574

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Example 1: Write the prime factorization for 92400

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2: A)Determine the prime factors of 2646 and write the prime factorization using a factor tree.

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2: B) Determine the prime factors of 2646 and write the prime factorization using repeated division. (divide by prime numbers)

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3. Determine the prime factors of 6600 and write the prime factorization using repeated division. (divide by prime numbers)

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4. Determine the prime factors of 22869000 and write the prime factorization

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The greatest common factor of two or more numbers is the greatest factor that the numbers have in common. To determine the greatest common factor we have to factor all the given numbers or use prime factorization.

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Factor rainbow Example 1: Determine the greatest common factor of 126 and 144 by factoring each number.

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Using Prime Factorization Example 1: Determine the greatest common factor of 126 and 144 by factoring each number.

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Example 2: Determine the greatest common factor of 220 and 860 (using prime factorization).

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The greatest common factor (GCF) is equal to the product of all the prime numbers that are in EVERY prime factorization.

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Do #3-9 on page 141

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The least common multiple of a set of numbers is the least multiple that is divisible by each number. Example 5: Determine the least common multiple of 28 and 52 by listing their multiples.

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Example 6: Determine the least common multiple of 28,42, and 63 using prime factorization. (Hint: take the highest power found anywhere)

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To find the least common multiple (LCM) we have to determine the product of the greatest power of each prime factor.

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Pg 138 Example 4

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Example 7: What is the side length of the smallest square that could be tiled with rectangles that measure 8cm by 36cm. Sketch the square and rectangles. (we must find the least common multiple)

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Example 8: What is the side length of the largest square that could be used to tile a rectangle that measures 12in. by 50in. Sketch the rectangle and squares. (greatest common factor)

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Example 9: A bar of soap has the shape of a rectangular prism that measures 10cm by 6cm by 3cm. What is the edge length of the smallest cube that could be filled with these soap bars?

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Homework Pg 140 #10d,11a,17,19

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Prime Factorization (Factor Trees) Greatest Common Factor

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