1. Prime Factor Decomposition
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2. What is a prime number?
A prime number is a number with exactly 2 factors
The 2 factors of any prime number are:
number 1
the prime number itself 2, 3, 5, 7,
11,
13,
17,
19,
23,
29,
31,
37,
41,…
1 is not a prime number
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3. Prime Number Decomposition
FACT:
Every number can be written as a product of prime numbers [and number 1] 24
= 2 x 2 x 2 x 3
= 23 x 31 12 2 2 6 2 3 3 1
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4. Prime Number Decomposition30
= 2 x 3 x 5
= 21 x 31 x 51 15 2 3 5 5 1
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5. Prime Number Decomposition36
= 2 x 2 x 3 x 3
= 22 x 32 18 2 2 9 3 3 3 1
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6. Prime Number Decomposition48
= 2 x 2 x 2 x 2 x 3
= 24 x 31 24 2 2 12 2 6 2 3 3 1
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7. Prime Number Decomposition60
= 2 x 2 x 3 x 5
= 22 x 31 x 51 30 2 2 15 3 5 5 1
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8. Prime Number Decomposition72
= 2 x 2 x 2 x 3 x 3
= 23 x 32 36 2 2 18 2 9 3 3 3 1
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9. Prime Number Decomposition
120
= 2 x 2 x 2 x 3 x 5
= 23 x 31 x 51 60 2 2 30 2 15 3 5 5 1
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10. Prime Number Decomposition
168
= 2 x 2 x 2 x 3 x 7
= 23 x 31 x 71 84 2
With bigger numbers use a calculator 2 42 2 21 3 7 7 1
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11. Prime Number Decomposition
540
= 2 x 2 x 3 x 3 x 3 x 5
= 23 x 32 x 51 2
270
With bigger numbers use a calculator
135 2 45 3 3 15 3 5 5 1
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12. Class-Work
Decompose these numbers into their prime factors.
Write the final answer using powers 20 30 36 45 60 72 90
144
150
196
288
360
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13. © T Madas

14. Write these numbers as a product of prime factors12 18 24 2 2 2 6 9 12 2 3 2 3 3 6 3 3 2 1 1 3 3 1
12 = 2
x 2
x 3
18 = 2
x 3
x 3
24 = 2
x 2
x 2
x 3
12 = 22
x 3
18 = 2
x 32
24 = 23
x 3
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15. Write these numbers as a product of prime factors20 30 36 2 2 2 10 15 18 2 3 2 5 5 9 5 5 3 1 1 3 3 1
20 = 2
x 2
x 5
30 = 2
x 3
x 5
36 = 2
x 2
x 3
x 3
20 = 22
x 5
36 = 22
x 32
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16. Write these numbers as a product of prime factors45 60 72 5 2 2 9 30 36 3 2 2 3 15 18 3 3 2 1 5 9 5 3 1 3 3 1
45 = 3
x 3
x 5
60 = 2
x 2
x 3
x 5
72 = 2
x 2
x 2
x 3
x 3
45 = 32
x 5
60 = 22
x 3
x 5
72 = 23
x 32
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17. Write these numbers as a product of prime factors48 54 56 2 2 2 24 27 28 2 3 2 12 9 14 2 3 2 6 3 7 2 3 7 3 1 1 3 1
48 = 2
x 2
x 2
x 2
x 3
54 = 2
x 3
x 3
x 3
56 = 2
x 2
x 2
x 7
48 = 24
x 3
54 = 2
x 33
56 = 23
x 7
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18. Write these numbers as a product of prime factors84 90 80 2 2 2 42 45 40 2 5 2 21 9 20 3 3 2 7 3 10 7 3 2 1 1 5 5 1
84 = 2
x 2
x 3
x 7
90 = 2
x 3
x 3
x 5
80 = 2
x 2
x 2
x 2
x 5
84 = 22
x 3
x 7
90 = 2
x 32
x 5
80 = 24
x 5
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19. Write these numbers as a product of prime factors
100
210
108 2 2 2 50
105 54 2 5 2 25 21 27 5 3 3 5 7 9 5 7 3 1 1 3 3 1
100 = 2
x 2
x 5
x 5
210 = 2
x 3
x 5
x 7
108 = 2
x 2
x 3
x 3
x 3
100 = 22
x 52
108 = 22
x 33
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20. © T Madas

21. Write these numbers as a product of prime factors12 18 24 2 2 2 6 9 12 2 3 2 3 3 6 3 3 2 1 1 3 3 1
12 = 2
x 2
x 3
18 = 2
x 3
x 3
24 = 2
x 2
x 2
x 3
12 = 22
x 3
18 = 2
x 32
24 = 23
x 3
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22. Write these numbers as a product of prime factors20 30 36 2 2 2 10 15 18 2 3 2 5 5 9 5 5 3 1 1 3 3 1
20 = 2
x 2
x 5
30 = 2
x 3
x 5
36 = 2
x 2
x 3
x 3
20 = 22
x 5
36 = 22
x 32
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23. Write these numbers as a product of prime factors45 60 72 5 2 2 9 30 36 3 2 2 3 15 18 3 3 2 1 5 9 5 3 1 3 3 1
45 = 3
x 3
x 5
60 = 2
x 2
x 3
x 5
72 = 2
x 2
x 2
x 3
x 3
45 = 32
x 5
60 = 22
x 3
x 5
72 = 23
x 32
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24. Write these numbers as a product of prime factors48 54 56 2 2 2 24 27 28 2 3 2 12 9 14 2 3 2 6 3 7 2 3 7 3 1 1 3 1
48 = 2
x 2
x 2
x 2
x 3
54 = 2
x 3
x 3
x 3
56 = 2
x 2
x 2
x 7
48 = 24
x 3
54 = 2
x 33
56 = 23
x 7
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25. Write these numbers as a product of prime factors84 90 80 2 2 2 42 45 40 2 5 2 21 9 20 3 3 2 7 3 10 7 3 2 1 1 5 5 1
84 = 2
x 2
x 3
x 7
90 = 2
x 3
x 3
x 5
80 = 2
x 2
x 2
x 2
x 5
84 = 22
x 3
x 7
90 = 2
x 32
x 5
80 = 24
x 5
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26. Write these numbers as a product of prime factors
100
210
108 2 2 2 50
105 54 2 5 2 25 21 27 5 3 3 5 7 9 5 7 3 1 1 3 3 1
100 = 2
x 2
x 5
x 5
210 = 2
x 3
x 5
x 7
108 = 2
x 2
x 3
x 3
x 3
100 = 22
x 52
108 = 22
x 33
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27. © T Madas