Download Prime Factorization

Prime Factorization
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The Fundamental Theorem of Arithmetic states that every natural number greater than 1 can be
written as a unique product of prime numbers. Let’s see if we can find these prime factors.
We will start looking for our prime factors by dividing. There are three simple divisibility rules that
will help in our search for our prime factors. Consider these rules for dividing by the primes 2, 3 & 5.
Rule 1: A number is divisible by 2 if it is even (the last digit being 0, 2, 4, 6, or 8).
Rule 2: A number is divisible by 3 if the sum of its digits is divisible by 3.
Rule 3: A number is divisible by 5 if its last digit is 0 or 5.
Example: The number 96 is divisible by 2 and 3. It is divisible by 2 because 96 is even and by 3 since
9 + 6 = 15 which is divisible by 3.
Example: The number 910 is divisible by 2 and 5. It is divisible by 2 because 910 is even and by 5
since it ends in 0.
Directions: Remember to keep looking for factors until ALL of the factors are prime numbers.
1. State whether each number is divisible by 2, 3 and/or 5.
a) 324
b) 640
c) 805
2. a) Write 8 as the product of any two factors.
b) Write 8 as the product of prime factors.
3. Fill in the missing factors so that the number is expressed as a product of prime factors.
a) 28 = 2 i
i 7=2
b) 50 = 2 i
i7
4. Fill in the missing elements of this factor tree.
140
14
2
5
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i 5=2 i 5
5. Express as a product of primes:
a) 9
b) 40
c) 27
d) 75
e) 63
f) 200
g) 110
h) 136
i) 55
6. Express each number as a product of primes. Write your answer as powers of prime factors.
a) 3600
b) 3375
7. When 2, 3 and 5 are not prime factors, you may want to use your calculator to help you check for
prime factors such as 7, 11, 13, 17, 19 and higher. Using your calculator, express each of the
following as a product of primes.
a) 91
b) 2737
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