Prime Factorization
Method 1. Dividing by Primes
Begin with the smallest prime that divides the given number.
1) If the number is even, divide by 2 and continue to divide by 2
until an odd number results.
2) Next ,try 3,then 5,then 7,and so forth.
3) Stop when the when the result is a prime number.
Finding Prime Factorization
Example 6: Find the prime factorization of 54.
Because 54 is even, divide by 2:
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Stop when the number
is prime. |
The prime factors are
the divisors. |
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Write the prime factorization
Prime Factorization
Method 2. Using a Factor Tree
To prime factor a number with a factor tree,
1) Begin with any pair of factors of the given number.
2)Factor each branch.
3)Factor each succeeding branch, until each branch ends with
a prime number.
Example 6:Find the prime factorization of 150.
Factor Tree
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Factors of 150 |
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Prime factors of 150 |
Practice Exercise 2
Find the prime factorization of 60.
Check answer
Solution − Practice Exercise 2
Find the prime factorization of 60.
Answer: C
Practice Exercise 3
Find the prime factorization of 180.
Check answer
Solution − Practice Exercise 3
Find the prime factorization of 180.
Answer: B
Simplifying Fractions with Variables
Because a variable re presents some "number," we can cancel
variable
factors.
Example 7: Simplify 
To simplify the fraction , factor the numerator and
denominator .
Then cancel the common factors of 7 and y:
Practice Exercise 4
Simplify: 
C. Can't be simplified
Solution − Practice Exercise 5
Simplify: 
C. Can't be simplified
Answer: B
