Answer:
1. So, Kate can put 45 video games each in 13 shipping boxes or 13 video games each in 45 shipping boxes.
2. Kate can put 117 video games each in 5 shipping boxes or 5 video games each in 117 shipping boxes.
3. Kate can put 9 video games each in 65 shipping boxes or 65 video games each in 9 shipping boxes.
Step-by-step explanation:
The prime factorization of 585 = 3² × 5 × 13.
So, the number of video games Kate can put in each shipping box are the different combinations of the prime factors. So, they are
1. 3² × 5 × 13 = 45 × 13 or 13 × 45.
So, Kate can put 45 video games each in 13 shipping boxes or 13 video games each in 45 shipping boxes.
2. 3² × 5 × 13 = 3² × 13 × 5 = 117 × 5 or 5 × 117
So, Kate can put 117 video games each in 5 shipping boxes or 5 video games each in 117 shipping boxes.
3. 3² × 5 × 13 = 3² × 13 × 5 = 9 × 65 or 65 × 9
So, Kate can put 9 video games each in 65 shipping boxes or 65 video games each in 9 shipping boxes.
