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Prime Factors Slideshow 5, Mr Richard Sasaki, Room 307

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Objectives Recall the meaning and list of prime numbersRecall the meaning and list of prime numbers Understand how to calculate the product of prime factors for a numberUnderstand how to calculate the product of prime factors for a number Use prime factors to show whether a rooted number produces an integer.Use prime factors to show whether a rooted number produces an integer.

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Prime Numbers What are prime numbers? Prime numbers are numbers with only two factors, the number itself and 1. It’s useful to remember the first few prime numbers. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, … Obviously the list is infinite, but you should know the first ones. If we divide a number by numbers in this list, we can find its prime factors.

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Prime Factors An easy way to separate a number into a product of its prime factors is to create a prime factor tree. We try to divide the number by each of the prime numbers in the list and shrink it until it is only made of prime numbers. 60 2, 3, 5, 7, 11, … ② 30 ② 15 ③ ⑤

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Prime Factors Let’s try with a larger number , 3, 5, 7, 11, … ② 980 ② 490 ② 245 ⑤ 49 ⑦⑦ Try the worksheet!

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Answers – Questions ②6 ②③ 30 ②15 ③⑤ 50 ②25 ⑤⑤ 42 ②21 ③⑦ 75 ③25 ⑤⑤ 36 ②18 ②9 ③③

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Answers – Questions ②75 ③25 ⑤⑤ 770 ②385 ⑤77 ⑪⑦ 85 ⑤⑰ 4620 ② 2310 ② 1155 ③ 385 ⑤ 77 ⑦ ⑪ 189 ③63 ③21 ⑦③ 1001 ⑦ 143 ⑪⑬

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Example 4 4 We can also do this by using the number’s prime factors.

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Example Write 81 as a product of its prime factors and hence, show that 81 is a square number. 81 ③27 ③ 9 ③ ③

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Example 132 ②66 ② 33 ③ ⑪

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Answers – Question 1 9 ③ ③ 100 ② 50 ② 25 ⑤ ⑤ 132 ② 66 ② 33 ③ ⑪ 256 ② 128 ② 64 ② 32 ② 16 ② 8 ② 4 ② 400 ② 200 ② 100 ② 50 ② 25 ⑤ ⑤ 142 ② 71 ②

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Answers – Question ③ 75 ③ 25 ⑤ ⑤ 999 ③ 333 ③ 111 ③ ⑰ ⑰ 260 ② 130 ② 65 ⑤ ⑬ 784 ② 392 ② 196 ② 98 ② 49 ⑦ ⑦ 6258 ② 3129 ③ 1043 ⑦ 149

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