One table at a bake sale has 75 oatmeal cookies . Another table has 60 lemon cupcakes . Which table allows for more rectangular arrangements when all the cookies and cupcakes are displayed ? Explain .

list the pairs of factors of 60 and 75

The more factors, the more ways they can be arranged.

To find out which table allows for more rectangular arrangements, we need to determine which quantity has more factors. The number of factors for a number indicates how many rectangular arrangements can be made with that quantity.

To find the factors of 75, we can start by prime factorizing it. The prime factorization of 75 is 3 * 5^2. To find the factors, we can combine these prime factors in various ways. The factors of 75 are 1, 3, 5, 15, 25, and 75.

Now let's find the factors of 60. The prime factorization of 60 is 2^2 * 3 * 5. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Comparing the number of factors, we see that 60 has more factors than 75. This means that the table with 60 lemon cupcakes allows for more rectangular arrangements when all the cookies and cupcakes are displayed.