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Prime Factor Decomposition
© T Madas
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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 © T Madas
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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 © T Madas
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Prime Number Decomposition
30 = 2 x 3 x 5 = 21 x 31 x 51 15 2 3 5 5 1 © T Madas
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Prime Number Decomposition
36 = 2 x 2 x 3 x 3 = 22 x 32 18 2 2 9 3 3 3 1 © T Madas
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Prime Number Decomposition
48 = 2 x 2 x 2 x 2 x 3 = 24 x 31 24 2 2 12 2 6 2 3 3 1 © T Madas
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Prime Number Decomposition
60 = 2 x 2 x 3 x 5 = 22 x 31 x 51 30 2 2 15 3 5 5 1 © T Madas
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Prime Number Decomposition
72 = 2 x 2 x 2 x 3 x 3 = 23 x 32 36 2 2 18 2 9 3 3 3 1 © T Madas
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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 © T Madas
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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 © T Madas
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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 © T Madas
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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 © T Madas
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© T Madas
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Write these numbers as a product of prime factors
12 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 © T Madas
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Write these numbers as a product of prime factors
20 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 © T Madas
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Write these numbers as a product of prime factors
45 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 © T Madas
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Write these numbers as a product of prime factors
48 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 © T Madas
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Write these numbers as a product of prime factors
84 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 © T Madas
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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 © T Madas
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© T Madas
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Write these numbers as a product of prime factors
12 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 © T Madas
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Write these numbers as a product of prime factors
20 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 © T Madas
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Write these numbers as a product of prime factors
45 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 © T Madas
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Write these numbers as a product of prime factors
48 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 © T Madas
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Write these numbers as a product of prime factors
84 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 © T Madas
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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 © T Madas
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© T Madas
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