Final answer:
After calculating the number from its prime factorization (2 cubed times 3 squared times 5), we find that it is 360. By dividing 360 by each option, we conclude that the number is divisible by 60, 72, and 180, with the most specific correct answer being that the number is divisible by 72.
Step-by-step explanation:
The prime factorization of a number is 2 cubed times 3 squared times 5. To determine which statement about the factors of the number is true, we should calculate the number by multiplying the prime factors. This gives us 23 × 32 × 5 = 8 × 9 × 5 = 72 × 5 = 360. Therefore, we can divide 360 by each option to see which is a factor.
- Option 1: 360 ÷ 60 = 6, so the number is divisible by 60.
- Option 2: 360 ÷ 72 = 5, so the number is also divisible by 72.
- Option 3: 360 ÷ 180 = 2, so the number is also divisible by 180.
- Option 4: 360 ÷ 720 is not a whole number, so the number is not divisible by 720.
Thus, Options 1, 2, and 3 are correct but since the question indicates there is only one true statement, Option 2 is the most specific correct answer: The number is divisible by 72.