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: 26

Answer

$48 = 2\cdot 2\cdot 2\cdot 2\cdot3$

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 $48$ we write the number as a product of factors and continue the process until all factors are prime numbers. We start by writing $48$ as a product of two numbers: $48=2\cdot 24$. The number $2$ is prime, but $24$ is not. So we write $24=2\cdot 12$: $48=2\cdot 2\cdot 12$. As $12$ is not a prime number we write: $12=2\cdot 6$ and we have: $48=2\cdot 2\cdot 2\cdot 6$. As $6$ is not a prime number we write: $6=2\cdot 3$ and we have: $48=2\cdot 2\cdot 2\cdot 2\cdot 3$. Now each factor is a prime number, therefore the prime factorization of $48$ is $2\cdot 2\cdot 2\cdot 2\cdot 3$.
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