# 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. Which of the following is not a prime factorization? a) 20 = 2�10 , b) 14 = 2�7 , 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 = 2�10 ; 10 is not a prime number. c) 64 = 4 3 ; 4 is not a prime number. 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 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 A�B? Solution Prime factorization. A�B = (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 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 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