Solutions to Questions on Prime Factorization

Detailed solutions to the questions on Prime Factorization are presented.

A Prime Factors Calculator may be used to check your answers.


Answer the following questions on prime factorization.

  1. Which of the following is not a prime factorization?
    a) 20 = 210 , b) 14 = 27 , c) 64 = 4 3 , d) 120 = 2 3 15
    Solution
    Prime factorization involves only prime numbers. Hence The following are not prime factorization.
    a) 20 = 210 ; 10 is not a prime number.
    c) 64 = 4 3 ; 4 is not a prime number.
  2. What is the prime factorization of the following numbers?
    a) 28 , b) 32 , c) 100 , d) 126 , e) 900
    Solution
    Prime factorization of the above are.
    a) 28 = 2 2 7 = 2 2 7
    b) 32 = 2 2 2 2 2 = 2 5
    c) 100 = 2 2 5 5 = 2 2 5 2
    d) 126 = 2 3 3 7 = 2 3 2 7
    e) 900 = 2 2 3 3 5 5 = 2 2 3 2 5 2
  3. Two numbers A and B are given by: A = 2 3 5 2 11 and B = 2 2 5 13. What is the prime factorization of AB?
    Solution
    Prime factorization.
    AB = (2 3 5 2 11 ) (2 2 5 13) = 2 2 2 5 5 11 2 2 5 13
    = 2 5 5 3 11 13

  4. Find the prime factorization of 100 and 70 and then the prime factorization of 7000 knowing that 7000 = 100 70
    Solution
    Prime factorization of 100 and 70.
    100 = 2 2 5 2
    70 = 2 5 7
    Use the fact that 7000 = 100 70 to find the prime factorization 7000.
    7000 = 100 70 = (2 2 5 2) (2 5 7) = 2 2 5 5 2 5 7 = 2 3 5 3 7
  5. a) Find the prime factorization of 10.
    b) Use the result in part a) and the fact that 100 = 10 10 to find the prime factorization of 100.
    c) Use the result in part a) and the fact that 1000 = 10 10 10 to find the prime factorization of 1000.
    d) Use the results in parts a), b) and c) to find a pattern of prime factorization and find the prime factorization of 1000,000.
    Solution
    a) Prime factorization of 10.
    10 = 2 5
    b) Prime factorization of 100.
    100 = 10 10 = 10 2 = (2 5) (2 5) = 2 2 5 2
    c) Prime factorization of 1000.
    1000 = 10 10 10 = 10 3 = (2 5) (2 5) (2 5) = 2 3 5 3
    d) Prime factorization of 1000,000 using the above pattern.
    1000,000 = 10 6 = 2 6 5 6


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