Question

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

Prime factorization of 48: 2 x 2 x 2 x 2 x 3
Prime factorization of 72: 2 x 2 x 2 x 3 x 3

The greatest common factor is 2 ´ 2 ´ 2 ´ 3 x 3

What is Ryan’s error?
Ryan did not add the common prime factors to get the greatest common factor.
Ryan did not list all the factors in the prime factorization of 48.
Ryan did not list all the factors in the prime factorization of 72.
Ryan did not include only common prime factors in the greatest common factor.

1. thachthao

2. thienthanh
The greatest common factor of 48 and 72 is 2 x 2 x 2 x 3 so Ryan did not include only common prime factors in the greatest common factor.

### What is the highest common factor?

The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.
In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.
For example in 6 and 12 6 is the highest common factor.
The Prime factorization of 48: 2 x 2 x 2 x 2 x 3
The Prime factorization of 72: 2 x 2 x 2 x 3 x 3
So common factors are ( 2 x 2 x 2)  x 3
Since 3 is the only factor in 48 so Ryan did not include its only common factor he includes 3 x 3 which is not present in the  Prime factorization of 48.
Hence “The greatest common factor of 48 and 72 is 2 x 2 x 2 x 3 so Ryan did not include only common prime factors in the greatest common factor”.