Determine the prime factorization of the following number:

\[13915\]

Start by dividing the number by the first prime number, which is $2$. If there is no remainder., it means you can divide evenly, then \[2\] is a factor of the number. Continue dividing by $2$ until you cannot divide evenly anymore. Write down how many \[2's\] you were able to divide the number by evenly. Now try dividing by the next prime factor, which is \[3\] . Ultimately the goal is to get to a quotient of \[1\].

\[13,915{\text{ }} \div {\text{ }}2{\text{ }} = {\text{ }}6,957.5\] - This has a remainder. Let's try another prime number.

\[13,915{\text{ }} \div {\text{ }}3{\text{ }} = {\text{ }}4,638.3333\] - This has a remainder. Let's try another prime number.

\[13,915{\text{ }} \div {\text{ }}5{\text{ }} = {\text{ }}2,783\] - There is no remainder. Hence, \[5\] is one of the factors.

\[2,783{\text{ }} \div {\text{ }}5{\text{ }} = {\text{ }}556.6\] - There is a remainder. We can't divide by \[5\] evenly anymore. Let's try the next prime number.

\[2,783{\text{ }} \div {\text{ }}7{\text{ }} = {\text{ }}397.5714\] - This has a remainder. \[7\] is not a factor.

\[2,783{\text{ }} \div {\text{ }}11{\text{ }} = {\text{ }}253\] - There is no remainder. Hence, \[11\] is one of the factors.

\[253{\text{ }} \div {\text{ }}11{\text{ }} = {\text{ }}23\] - There is no remainder. Hence, \[11\] is one of the factors.

\[23{\text{ }} \div {\text{ }}11{\text{ }} = {\text{ }}2.0909\] - There is a remainder. We can't divide by \[11\] evenly anymore. Let's try the next prime number

\[23{\text{ }} \div {\text{ }}13{\text{ }} = {\text{ }}1.7692\] - This has a remainder. \[13\] is not a factor.

\[23{\text{ }} \div {\text{ }}17{\text{ }} = {\text{ }}1.3529\] - This has a remainder. \[17\] is not a factor.

\[23{\text{ }} \div {\text{ }}19{\text{ }} = {\text{ }}1.2105\] - This has a remainder. \[19\] is not a factor.

\[23{\text{ }} \div {\text{ }}23{\text{ }} = {\text{ }}1\] - There is no remainder. Hence, \[23\] is one of the factors.

The prime factors of the given number are $5$, $11$, $23$.

As we can see, we can write $13915$ as $5 \times 11 \times 11 \times 23$. It can also be written in exponential form as ${5^1} \times {11^2} \times {23^1}$.

dividing the number into smaller parts.