Section 2.2 Prime Numbers and Factorization 109 Prime factorizations of numbers will be particularly helpful when we add, subtract, multiply, divide, and simplify fractions. Determining the Prime Factorization of a Number Example 4 Find the prime factorization of 220. Solution: One method to factor a whole number is to make a factor tree. Begin by determining any two numbers that when multiplied equal 220. Then continue factoring each factor until the branches “end” in prime numbers. 220 10 22 5 2 2 11 Branches end in prime numbers. Therefore, the prime factorization of 220 is 2 2 5 11. TIP: The prime factorization from Example 4 can also be expressed by using exponents as 22 5 11. In Example 4, note that the result of a prime factorization does not depend on the original two-number factorization. Similarly, the order in which the factors are written does not affect the product, for example, 220 11 20 2 10 2 5 220 4 55 2 2 5 11 220 2 110 2 55 5 11 220 2 2 5 11 220 2 2 5 11 220 11 2 2 5 TIP: You can check the prime factorization of any number by multiplying the factors. Answer 9. 2 3 3 5 Another technique to find the prime factorization of a number is to divide the number by the smallest known prime factor.Then divide the quotient by its smallest known prime factor. Continue dividing in this fashion until the quotient is a prime number. The prime factorization is the product of divisors and the final quotient. For example, 2 is the smallest prime factor of 220 2 is the smallest prime factor of 110 5 is the smallest prime factor of 55 the last quotient is prime 2)220 2)110 5)55 11 Therefore, the prime factorization of 220 is 2 2 5 11 or 22 5 11. Skill Practice 9. Find the prime factorization of 90. Avoiding Mistakes Make sure that the end of each branch is a prime number.
miller_basic_college_math_3e_ch1_3
To see the actual publication please follow the link above