Question

What is a prime factor tree of 16?

Answer 1

Hint: We first explain the prime factorisation of the number 16. We find the multiplied form using the normal factorisation. Then we use the tree form of prime factorisation to form the image where we keep diving until we can't factor any more.

Complete step by step solution:
The given number is 16. We have to find the prime factor tree of 16.
A prime factor tree is a tree shaped diagram, where one finds the factors of a number, then the factors of those numbers, until one can't factor any more. 
First find the prime factorisation of 16 in the normal factorisation process.
$\begin{align}
  & 2\left| \!{\underline {\,
  16 \,}} \right. \\
 & 2\left| \!{\underline {\,
  8 \,}} \right. \\
 & 2\left| \!{\underline {\,
  4 \,}} \right. \\
 & 2\left| \!{\underline {\,
  2 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
Therefore, the prime factorisation of 16 becomes $16=2\times 2\times 2\times 2={{2}^{4}}$.
Now we express the tree process where we take the divisors on the left side and write down the quotient just under the previous dividend.
Therefore, we first divide with 2 and get 8. We continue this process 2 more times. The consecutive quotients are 4, 2. So, now we draw the prime factor tree for 16.

Note: The division and tree process of prime factorisation is totally similar to the division form but the representations are different. In case of the tree prime factorisation, 16 will also be expressed as $16=2\times 2\times 2\times 2={{2}^{4}}$.