Question

Use a factor tree to find the prime factors of $72$. Write the prime factorization using exponents ?

Answer 1

Hint: To get the Prime factors of $72$, you have to divide $72$ by the smallest prime number possible. Then you take the result from that and divide that by the smallest prime number. Repeat this process until you get the prime number.

Complete step-by-step solution:
To find the prime factorization of $72$ , the procedure below applies to find prime factorization of a number.
We need to find $2$ factors of the given number, determine if at least one of them is not prime; if it is not a prime factor it repeats this process until all factors are prime.
Here to find the prime factorization of $72$ the broad factors are $8$ and $9$. Then we proceed as given below. Then factors tree comes up as shown below:

Hence, there are total $5$ prime factors of $72$ , they are
$ \Rightarrow 2 \times 2 \times 2 \times 3 \times 3 = {2^3} \times {3^2}$.

Note: The key point to make a factor tree is to factorize the given number until we get a prime number. In the given question when we count the number of prime numbers above, we find that $72$ has a total of $5$ prime factors. When you multiply all the prime factors of $72$ together it will result in $72$ .
This is called the product of prime factors of $72$ .
Additional information: A factor tree is a diagram in which you first have broad factors of a number and so on, until you can’t factor anymore and you have all the prime factors at the end.