sally drew a factor tree of a composite number and ended up with 4x4x5x5x3 as the prime factorization.
explain what is wrong with this factorization
1. what is the correct prime factorization?
2. what is the composite number that was factored?
4 is not a prime
2x2x2x2x3x5x5 or 2^4•3•5^2
(usually the primes are listed in increasing order)
It always starts from the lowest to the highest 1)the correct factor= 2*2*2*2*3*5*5 (2) 1200 is the composite factor
The correct prime factorization of a number is a representation of that number as a product of its prime factors. In the given factor tree, Sally arrived at the factorization 4x4x5x5x3 for a composite number. However, there are a couple of errors in this factorization.
1. The first error is that 4 is not a prime number. It can be further factorized as 2x2. So, the correct prime factorization of 4 should be 2x2 instead of 4.
2. The second error is that 5 is not a factor of 4. So, there should not be any 5s in the factorization.
Taking these errors into account, let's calculate the correct prime factorization:
Start with the number 4x4x5x5x3:
1. Rewrite 4 as 2x2:
(2x2) x 4x5x5x3
2. Simplify the expression inside the parentheses:
2x2 x 100x3
3. Multiply the common factors:
4x300
Therefore, the correct prime factorization is 2x2x3x5x5x3.
To find the composite number that was factored, we multiply the prime factors together:
Composite number = 2 x 2 x 3 x 5 x 5 x 3
Composite number = 1800
So, the composite number that was factored is 1800.