A caterer is planning a large party for 1001 guest. Each table must seat an equal number of guest , more than 1 guest and fewer than 20. Determine the number of tables if the caterer uses 13 person tables. How many tables will they need.

there are blank possible table sizes that will seat an equal number of guest more than 1 guest and fewer than 20?

To determine the number of tables needed, we need to find the total number of guests and divide it by the number of guests each table can seat. Let's calculate:

Total number of guests = 1001
Number of guests each table can seat = 13

Number of tables needed = Total number of guests / Number of guests each table can seat

Number of tables needed = 1001 / 13

To calculate this, we can use division or rounded division.

If we do a rounded division, we can use the formula: rounded division = ceil(Total number of guests / Number of guests each table can seat). This will ensure that we have enough tables to accommodate all the guests.

So, the number of tables needed = ceil(1001 / 13) = ceil(77.000) = 77

Therefore, the caterer will need 77 tables to accommodate the 1001 guests.

Now, let's determine the possible table sizes that will seat an equal number of guests more than 1 and fewer than 20.

Given that each table can seat more than 1 guest and fewer than 20, we need to find all the positive divisors (factors) of a number between 1 and 20.

Divisors of 20: 1, 2, 4, 5, 10, 20
Divisors of 19: 1, 19
Divisors of 18: 1, 2, 3, 6, 9, 18
Divisors of 17: 1, 17
Divisors of 16: 1, 2, 4, 8, 16
Divisors of 15: 1, 3, 5, 15
Divisors of 14: 1, 2, 7, 14
Divisors of 13: 1, 13
Divisors of 12: 1, 2, 3, 4, 6, 12
Divisors of 11: 1, 11
Divisors of 10: 1, 2, 5, 10
Divisors of 9: 1, 3, 9
Divisors of 8: 1, 2, 4, 8
Divisors of 7: 1, 7
Divisors of 6: 1, 2, 3, 6
Divisors of 5: 1, 5
Divisors of 4: 1, 2, 4
Divisors of 3: 1, 3
Divisors of 2: 1, 2

From the list of divisors, we can see that the possible table sizes that will seat an equal number of guests, more than 1 guest, and fewer than 20 are: 2, 4, 5, 6, 8, 10, 12, 14, 15, 16, 18, and 20.