Question

The work that Ryan did to find the greatest common factor of 48 and 72 is shown below.

Prime factorization of 48: 2x2x2x2x3
Prime factorization of 72: 2x2x2x3x3

The greatest common factor is 2'2'2'3x3

What is Ryan's error?

(A) Ryan did not add the common prime factors to get the greatest common factor
(B) Ryan did not list all the factors in the prime factorization of 48
(C) Ryan did not list all the factors in the prime factorization of 72
(D) Ryan did not include only common prime factors in the greatest common factor

Answer 1

The answer is A ryan did not add the common prime factors

Answer 2

The work that Ryan did to find the greatest common factor of 48 and 72 has no error, and Ryan found the least common multiple.

What is GCF (the greatest common factor)?

GCF or greatest common factor is the common number that all the term has in a group of terms.

The work that Ryan did to find the greatest common factor of 48 and 72 is shown below.

Prime factorization of 48: 2,2,2,2,3

Prime factorization of 72: 2,2,2,3,3

The greatest common factor is 2 ' 2 ' 2 ' 2 ' 3 ' 3

Here, the greatest common factor found is 2 ' 2 ' 2 ' 2 ' 3 ' 3 which is,

The number 144 is divisible by 48 and 72 in 3 times and 2 times respectively.

Thus, the work that Ryan did to find the greatest common factor of 48 and 72 has no error, and Ryan found the least common multiple.