Prime FactorsSlideshow 5, Mr Richard Sasaki, Room 307

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.

Prime NumbersWhat 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.

Prime FactorsAn 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.

602, 3, 5, 7, 11, …

② 30② 15

③ ⑤22×3×5=60

Prime FactorsLet’s try with a larger number.

1960

2, 3, 5, 7, 11, …② 980

② 490

② 245

⑤ 49⑦ ⑦

23×5×72=1960Try the worksheet!

Answers – Questions 1 - 6 12

② 6② ③

22×3=12

30② 15

③ ⑤2×3×5=30

50② 25

⑤ ⑤2×52=50

42② 21

③ ⑦2×3×7=4 2

75③ 25

⑤ ⑤3×52=75

36② 18

② 9

22×32=36

③③

Answers – Questions 7 - 12150

② 75③ 25

2×3×52=150⑤⑤

770② 385

⑤ 77

2×5×7×11=770⑪⑦

85⑤ ⑰

5×17=85

4620② 2310

② 1155③ 385

⑤ 77⑦ ⑪

22×3×5×7×11=4620

189③ 63

③ 21⑦③

33×7=189

1001⑦ 143

⑪ ⑬

7×11×13=1001

Writing in the form If we can write a number in the form where , then .ExampleShow 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.

Writing in the form ExampleWrite 81 as a product of its prime factors and hence, show that 81 is a square number.

81③ 27

③ 9③ ③

34=81()2=813×3

As we expressed 81 in the form , it must be square.

Writing in the form ExampleWrite 132 as a product of its prime factors and show that is not an integer.

132② 66

② 33③ ⑪

22×3×11=132

We cannot write in the form so 132 is not an integer.

Answers – Question 19

③ ③

32=9

100② 50

② 25⑤ ⑤

22×52=102

132② 66

② 33③ ⑪

22×3×11≠𝑏2256② 128

② 64② 32② 16

② 8② 4②

28=162

400② 200② 100② 50

② 25⑤ ⑤

24×52=202

142② 71

2×71≠𝑏2

②

Answers – Question 2225

③ 75③ 25⑤ ⑤

32×52=152

999③ 333③ 111③ 37

33×37≠𝑏2

289⑰ ⑰

172=289260

② 130② 65

⑤ ⑬

22×5×13≠𝑏2784

② 392② 196② 98② 49⑦ ⑦24×72=282

6258②3129③1043

⑦ 149

2×3×7×149≠𝑏2