Question

Manuel created a factor tree and wrote the prime factorization of 60 shown below.

A factor tree of 60. 60 branches to 4 and 15. 15 branches to 3 and 5. The equation is 60 = 3 times 4 times 5.

What is Manuel’s error?

Answer 1

he did not find the prime factors of 4

Explanation:

Answer 2

The mistake made by Manuel was not reducing 4 as a product of its prime numbers. That is,
`2* 2 = 4`. 4 is a composite number and a product of 2 prime numbers.

Explanation:

The factors of a given entire numbers consists in simplifying it several times until an equivalent product of prime numbers is found. Let is show the procedure for 60:

1)
`60` Given

2)
`15 * 4 = 60` Definition of multiplication.

3)
`(5* 3)* (2* 2) = 60` Definition of multiplication.

4)
`(2* 2)* (3* 5) = 60` Commutative property/Result.

The mistake made by Manuel was not reducing 4 as a product of its prime numbers. That is,
`2* 2 = 4`. 4 is a composite number and a product of 2 prime numbers.