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Chapter 10: Problem 10

Write each of the following integers as a product of prime numbers. a. 123 b. 375 c. 927

Short Answer

Expert verified
a. \(123 = 3 * 41\) \n b. \(375 = 5^3 * 3\) \n c. \(927 = 3^2 * 103\)

Step by step solution

01

Prime factorization for 123

First, find the smallest prime number that divides 123. We find that 3 is a factor of 123. So we divide 123 by 3 to get 41, which is a prime number itself. Thus, 123 can be represented as \(3 * 41\).
02

Prime factorization for 375

Next, we will find the smallest prime number that divides 375. We see that 5 is a factor of 375. So we divide 375 by 5 to get 75. Again, we divide 75 by 5 to get 15, and lastly, we divide 15 by 5 to get 3 which is a prime number. Thus, 375 can be represented as \(5 * 5 * 5 * 3\) or \(5^3 * 3\).
03

Prime factorization for 927

Lastly, we will find the smallest prime number that divides 927. We find that 3 is a factor of 927. After dividing 927 by 3, we get 309. Now, we divide 309 by 3 again to get 103 which is a prime number itself. Therefore, 927 can be represented as \(3 * 3 * 103\) or \(3^2 * 103\) .

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