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### Abstract Algebra: An Introduction

Book edition 3rd
Author(s) Thomas W Hungerford, David Leep
Pages 608 pages
ISBN 9781111569624

# Express each number as a product of primes:$\left(a\right)5040\phantom{\rule{0ex}{0ex}}\left(b\right)-2345\phantom{\rule{0ex}{0ex}}\left(c\right)45670\phantom{\rule{0ex}{0ex}}\left(d\right)2,042,040$

$\left(a\right)5040={2}^{4}×{3}^{2}×5×7\phantom{\rule{0ex}{0ex}}\left(b\right)-2345=1×5×7×67\phantom{\rule{0ex}{0ex}}\left(c\right)45670=2×5×4567\phantom{\rule{0ex}{0ex}}\left(d\right)2042040={2}^{3}×3×5×7×11×13×17$

See the step by step solution

## Step 1: Express the number as a product of prime

The prime divisors of number 5040 are 2, 3, 5, and 7.

Express 5040 as a product of primes as follows:

$\begin{array}{rcl}5040& =& 2·2·2·2·3·3·5·7\\ & =& {2}^{4}×{3}^{2}×5×7\end{array}$

Thus, $5040={2}^{4}×{3}^{2}×5×7$.

## Step 2: Express the number as a product of prime

The prime divisors of number are , 5, 7, and 67.

Express -2345 as a product of primes as follows:

$-2345=1×5×7×67$

Thus, $-2345=1×5×7×67$.

## Step 3: Express the number as a product of prime

The prime divisors of number 45670 are 2, 5, and 4567.

Express 45670 as a product of primes as follows:

$45670=2×5×4567$

Thus, $45670=2×5×4567$.

## Step 4: Express the number as a product of prime

The prime divisors of number 2042040 are 2, 3, 5, 7, 11, 13, and 17.

Express 2042040 as a product of primes as follows:

$\begin{array}{rcl}2042040& =& 2×2×2×3×5×7×11×13×17\\ & =& {2}^{3}×3×5×7×11×13×17\end{array}$

Thus, $2042040={2}^{3}×3×5×7×11×13×17$.