Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter R - Section R.1 - Factors and the Least Common Multiple - Exercise Set - Page R-7: 28

Answer

$64 = 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2$

Work Step by Step

The $\textit{prime factorization}$ of a number is obtained by writing the number as a product of primes. To determine the prime factorization of $64$ we write the number as a product of factors and continue the process until all factors are prime numbers. We start by writing $64$ as a product of two numbers: $64=2\cdot 32$. The number $2$ is prime, but $32$ is not. So we write $32=2\cdot 16$: $64=2\cdot 2\cdot 16$. As $16$ is not a prime number we write: $16=2\cdot 8$ and we have: $64=2\cdot 2\cdot 2\cdot 8$. As $8$ is not a prime number we write: $8=2\cdot 4$ and we have: $64=2\cdot 2\cdot 2\cdot 2\cdot 4$. As $4$ is not a prime number we write: $4=2\cdot 2$ and we have: $64=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2$. Now each factor is a prime number, therefore the prime factorization of $64$ is $2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2$.
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