Question

How do you make a factor tree showing the prime factorization of 7200?

Answer 1

Hint: To get the Prime Factors of 7200, you divide 7200 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 7200, 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 prime factorization of 7200 the broad factors are 72 and 100 and then we proceed as given below. Then factor tree comes up as shown below:

Hence, there are total 9 prime factors of 7200, they are \[2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5\]

Additional Information:
A factor tree is a diagram in which you first have broad factors of a number, then the factors of those numbers and so on, until you can't factor anymore and you have all the prime factors at the end. These prime factors at the end are all the prime factors of the original number and you can write the original number as a product of all prime numbers.

Note: The key point to make a factor tree is 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 7200 has a total of 9 Prime Factors. When you multiply all the Prime Factors of 7200 together it will result in 7200. This is called the Product of Prime Factors of 7200. Thus, the Prime Factors of 7200 are: 2, 2, 2, 2, 2, 3, 3, 5, 5.