Prime Factors

1. Prime Factors Slideshow 5, Mr Richard Sasaki, Room 307

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

3. Prime Numbers Prime numbers are numbers with only two factors, itself and 1. What are prime numbers? 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.

4. 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 15 ② ③ ⑤

5. Prime Factors 1960 Let’s try with a larger number. 2, 3, 5, 7, 11, … ② 980 490 ② ② 245 ⑤ 49 Try the worksheet! ⑦ ⑦

6. Answers 12 30 150 85 770 50 ② 6 ② 15 ② 75 ⑤ ⑰ ② 75 ② 25 ② ③ ③ ⑤ ③ 25 ⑤ 25 ⑤ ⑤ ⑤ ⑤ ⑦ ⑪ 75 36 42 1001 4620 189 ③ 25 ② 18 ② 21 ② 2310 ⑦ 143 ⑤ ⑤ ② 9 ③ 63 ② 1155 ③ ⑦ ⑪ ⑬ ③ 385 ③ ③ ③ 21 ⑤ 77 ③ ⑦ ⑪ ⑦

7. Writing in the form If we can write a number in the form where is an integer, then must produce an integer. Example Show that produces an integer. As 16 = 2, must be an integer ( =). 4 4 We can also do this by using the number’s prime factors.

8. Writing in the form Example Write 81 as a product of its prime factors and hence, show that 81 is a square number. 81 ③ 27 9 ③ ③ ③ As we expressed 81 in the form , it must be square.

9. Writing in the form Example Write 132 as a product of its prime factors and show that is not an integer. 132 ② 66 33 ② ③ ⑪ We cannot write in the form so 132 is not an integer.

10. Answers 132 9 289 100 225 999 ② 66 ⑰ ⑰ 75 ③ 333 ③ ② 50 ③ ③ ② 33 25 ③ 111 ③ ② 25 ③ ⑤ ⑪ ⑤ 37 ③ ⑤ ⑤ 6258 400 256 142 784 260 3129 ② 200 ② 71 ② ② 128 1043 392 ③ ② 130 ② 100 ② ② 64 196 ② 149 ⑦ 65 ② 50 ② ② 32 98 ② ⑬ ⑤ 25 ② ② 16 49 ② ⑤ ⑤ ② 8 ⑦ ⑦ ② 4 ② ②