We want to know if our friend is correct. To do so, remember that a factor tree is complete when only prime factors appear in the product. A prime number is a whole number greater than 1 with exactly two factors, 1 and itself. Notice that the factor tree our friend drew ends with 9. The number 9 is not a prime number because we can also divide it by 3.
9/3=3
This means that our friend did not complete the factor tree and that they are not correct.
Alternative Solution
Correct Solution
Let's find the correct prime factorization of 72. To do so, we will construct a new factor tree.
The prime factorization will be equal to the product of all the circled prime factors.
72=2* 2 * 2 * 3 * 3
We can rewrite this as a power by recalling that the base of a power is the repeated factor and the exponent is the number of times the base is used as a factor.
72=2^3 * 3^2
Notice that since 3^2=9, we actually get the same result as our friend. However, only our answer is correct because all of our factors are prime numbers.
