Question

Use the prime factorization to list all of its factors.

240

Short answer

The list of all the factors of 240 is:

$1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,and240.$.

Step-by-step solution

  Define prime factorization

When a number is written as a product of prime numbers it is defined as prime factorization, wherein, prime numbers are defined as whole numbers that is greater than 1 and has exactly two whole number factors 1 and itself.

  State the concept of prime factorization

Calculate the factors by dividing every possible number. Then take the result from that and divide that by the smallest prime number. Repeat this process until you end up with the smallest possible prime number.

  Factor the monomial

Expand 240 as per one possible factor tree $24\times 10$and get,

$\begin{array}{c}240\\ \begin{array}{cc}\swarrow & \searrow \end{array}\\ \begin{array}{ccc}24& \times & 10\end{array}\\ \begin{array}{cc}\swarrow \searrow & \swarrow \searrow \end{array}\\ \begin{array}{ccc}\underset{\begin{array}{l}\downarrow \\ 2\end{array}}{2}\times \underset{\begin{array}{l}\downarrow \\ 2\times 3\end{array}}{6}& \times & \underset{\begin{array}{l}\downarrow \\ 2\end{array}}{2}\times \underset{\begin{array}{l}\downarrow \\ 5\end{array}}{5}\end{array}\end{array}$

The prime factorization of $240=2^3\times 3\times 5$. Therefore, the list of the factors of 240 is:

$1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,and240.$