1. **State the problem:** We want to find the greatest number of cards per page such that the 54 hockey cards, 72 baseball cards, and 63 basketball cards can each be evenly divided onto pages. Then we determine how many pages are needed for each sport. 2. **Identify the question:** Find the greatest number of cards per page common to all three sets. This means we need the greatest common divisor (GCD) of 54, 72, and 63. 3. **Calculate the prime factorizations:** - 54 = $2 \times 3^3$ - 72 = $2^3 \times 3^2$ - 63 = $3^2 \times 7$ 4. **Find the GCD by taking the minimum power of common prime factors:** - Common prime factors: 3 - Minimum power of 3 among the three numbers: $3^2 = 9$ So, the greatest number of cards per page is $9$. 5. **Calculate the number of pages for each sport:** - Hockey: $\frac{54}{9} = 6$ pages - Baseball: $\frac{72}{9} = 8$ pages - Basketball: $\frac{63}{9} = 7$ pages **Final answer:** The greatest number of cards per page is $9$. We will need $6$ pages for hockey, $8$ pages for baseball, and $7$ pages for basketball.