# Slideshow 5, Mr Richard Sasaki, Room 307

## Presentation on theme: "Slideshow 5, Mr Richard Sasaki, Room 307"— Presentation transcript:

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

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, … 30 2 2 ×3×5=60 15

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

Answers – Questions 1 - 6 12 30 50 ② 6 ② 15 ② 25 ② ③ ③ ⑤ ⑤ ⑤ 2 2 ×3=12
2×3×5=30 2× 5 2 =50 75 36 42 25 18 21 9 3× 5 2 =75 2×3×7=42 2 2 × 3 2 =36

Answers – Questions 7 - 12 150 770 85 ② 75 ② 385 ⑤ ⑰ ③ 25 ⑤ 77 5×17=85
2× 3×5 2 =150 2×5×7×11=770 1001 4620 189 143 2310 63 1155 385 21 7×11×13 =1001 77 2 2 ×3×5×7×11=4620 3 3 ×7=189

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

Writing 𝑎 in the form 𝑏 2 Example
Write 81 as a product of its prime factors and hence, show that 81 is a square number. 81 3 4 =81 27 2 =81 3×3 9 As we expressed 81 in the form 𝑎×𝑏×…×𝑥 2 , it must be square.

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

Answers – Question 1 9 ② ② ③ ③ ② ② 3 2 =9 Square ③ ⑤
132 100 66 50 33 25 3 2 =9 Square 2 2 ×3×11≠ 𝑏 2 Not square 2 2 × 5 2 = Square 256 400 128 200 142 64 100 71 32 50 2×71≠ 𝑏 2 Not square 2 8 = Square 16 25 8 4 2 4 × 5 2 = Square

Answers – Question 2 999 289 225 ③ 75 ③ 333 ⑰ ⑰ ③ 25 ③ 111
17 2 =289 Integer 37 3 2 × 5 2 = Integer 3 3 ×37≠ 𝑏 2 Not integer 6258 260 3129 130 784 1043 65 392 196 149 2 2 ×5×13≠ 𝑏 2 Not integer 98 49 2 4 × 7 2 = Integer 2×3×7×149≠ 𝑏 2 Not integer

Download ppt "Slideshow 5, Mr Richard Sasaki, Room 307"

Similar presentations