Question

Express each number as a product of primes:

$$\begin{gathered} \left(a\right)5040 \\ \left(b\right)-2345 \\ \left(c\right)45670 \\ \left(d\right)2,042,040 \end{gathered}$$

Short answer

$$\begin{gathered} \left(a\right)5040=2^4\times 3^2\times 5\times 7 \\ \left(b\right)-2345=1\times 5\times 7\times 67 \\ \left(c\right)45670=2\times 5\times 4567 \\ \left(d\right)2042040=2^3\times 3\times 5\times 7\times 11\times 13\times 17 \end{gathered}$$

Step-by-step solution

Express the number as a product of prime 

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

Express 5040 asaproduct of primes asfollows:

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

Thus, $5040=2^4\times 3^2\times 5\times 7$.

Express the number as a product of prime

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

Express -2345 asaproduct of primes asfollows:

$-2345=1\times 5\times 7\times 67$

Thus, $-2345=1\times 5\times 7\times 67$.

Express the number as a product of prime

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

Express 45670 asaproduct of primes asfollows:

$45670=2\times 5\times 4567$

Thus, $45670=2\times 5\times 4567$.

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 asa product of primes asfollows:

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

Thus, $2042040=2^3\times 3\times 5\times 7\times 11\times 13\times 17$.