Whole Number Arithmetic Factors and Primes. Exercise 5 - Oral examples { factors of 15 } { factors...
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Transcript of Whole Number Arithmetic Factors and Primes. Exercise 5 - Oral examples { factors of 15 } { factors...
Exercise 5 - Oral examples
{ factors of 15 }
{ factors of 32 }
{ factors of 27 }
{ factors of 28 }
(1, 3, 5, 15)
(1, 2, 4, 8, 16, 32)
(1, 3, 9, 27)
(1, 2, 4, 7, 14, 28)
Exercise 5 - Written examples
1) { factors of 4 }2) { factors of 9 }3) { factors of 16 }4) { factors of 25 }5) { factors of 36 } 6) { factors of 1 } 7) { factors of 6 } 8) { factors of 12}
• (1, 2, 4)• (1, 3, 9)• (1, 2, 4, 8, 16)• (1, 5, 25)• (1, 2, 3, 4, 6, 9, 12, 18, 36)
• (1)• (1, 2, 3, 6)• (1, 2, 3, 4, 6, 12)
Exercise 5 - Written examples
9) { factors of 18 }10) { factors of 24 }11) { factors of 10 }12) { factors of 20 }13) { factors of 30 } 14) { factors of 40 } 15) { factors of 2 } 16) { factors of 3}
• (1, 2, 3, 6, 9, 18)• (1, 2, 3, 4, 6, 8, 12, 24)
• (1, 2, 5, 10)• (1, 2, 4, 5, 10, 20)• (1, 2, 3, 5, 6, 10, 15, 30)• (1, 2, 4, 5, 8, 10, 20, 40)
• (1, 2,)• (1, 3)
Exercise 5 - Written examples
17) { factors of 5 }18) { factors of 7}19) { factors of 11 }20) { factors of 13 }
• (1, 5)• (1, 7)• (1, 11)• (1, 13)
Prime Numbers
1) Prime numbers have exactly 2 factors ( namely 1 and itself).2)If a factor is a prime number then it is called a prime factor.
{ factors of 100 } = {1, 2, 4, 5, 10, 20, 25, 50, 100 }
{ prime factors of 100 } = { 2, 5 }
Exercise 5 - Written examples
21) { prime numbers between 0 and 10 }
22) { prime numbers between 10 and 20 }
23) { prime numbers between 20 and 30 }
24) { prime numbers between 30 and 40 }
• (2, 3, 5, 7)
• (11, 13, 17, 19)
• (23, 29)
• (31, 37)
32) { prime factors of 42 }
Factors of ‘42’ are 1, 2, 3, 6, 7, 14, 21, 42
Prime factors of ‘42’ are 2, 3, 7
Multiples
33) { multiples of 3 }
34) { multiples of 6 }
35) { multiples of 2 }
36) { multiples of 4 }
• 3, 6, 9, 12, …• 6, 12, 18, 24,,…• 2, 4, 6, 8, …• 4, 8, 12, 16, …
41) { factors of 60 }
42) { factors of 360 }
43) { prime numbers between 40 and 50 }
44) { prime numbers between 50 and 60 }
• (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
• (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360)
• (41, 43, 47)• (53, 59)
Exercise 6Write these numbers as products of their primes
1) 6
2) 10
3) 14
4) 15
5) 21
6) 35
7) 30
8) 70
• 2 x 3• 2 x 5• 2 x 7• 3 x 5• 3 x 7• 5 x 7• 2 x 3 x 5• 2 x 5 x 7
Exercise 6
9) 4
10) 8
11) 16
12) 32
13) 9
14) 27
15) 25
16) 49
• 2 x 2 = 22
• 2 x 2 x 2 = 23
• 2 x 2 x 2 x 2 = 24 • 25
• 3 x 3 = 32
• 3 x 3 x 3 = 33
• 5 x 5 = 52
• 7 x 7 = 72
Exercise 6
17) 12
18) 18
19) 20
20) 50
21) 45
22) 75
23) 36
24) 60
• 2 x 2 x 3 = 22 x 3• 2 x 3 x 3 = 2 x 32
• 2 x 2 x 5 = 22 x 5 • 2 x 5 x 5 =2 x 52
• 5 x 3 x 3 = 5 x 32
• 3 x 5 x 5 = 3 x 52
• 2 x 2 x 3 x 3 = 22 x 32
• 2 x 2 x 3 x 5 = 22 x 3 x 5
Exercise 6
25) 24
26) 54
27) 40
28) 56
29) 48
30) 80
31) 90
32) 84
• 23 x 3• 2 x 33
• 23 x 5 • 7 x 23
• 24 x 3• 24 x 5• 2 x 32 x 5• 22 x 3 x 7
Exercise 6
33) Find the smallest number which is the product of 4 different prime factors.
• 2 x 3 x 5 x 7 = 210
Exercise 6 - 34
• Find the next smallest number which is the product of 4 different prime factors.
• 2 x 3 x 5 x 11 = 330
Exercise 6 - 35
Find the smallest number which is the product of 4 prime factors (not necessarily different).
• 2 x 2 x 2 x 2 = 16