Final answer:
There are 7 factors of 64: 1, 2, 4, 8, 16, 32, and 64. These factors indicate the number of rectangular arrays Margie can make with steppingstones, showing that there are 7 different array dimensions she could create.
Step-by-step explanation:
To find out how many factors there are for the number 64, we need to identify all the integers that can multiply together to give us the product 64. This means we're looking for all the pairs of numbers that when multiplied will result in 64. Since 64 is a power of 2, it has more factors than a number that is not a power of 2.
Let's list all the factors of 64:
- 1 (1 x 64)
- 2 (2 x 32)
- 4 (4 x 16)
- 8 (8 x 8)
- 16 (16 x 4)
- 32 (32 x 2)
- 64 (64 x 1)
So, there are 7 factors of 64 in total. When it comes to arrays that Margie can make with her steppingstones, the number of factors determines the number of possible rectangular arrays she can form since each pair of factors gives a different array dimension.
As we notice, the number of factors of 64 is indicative of how many arrays Margie can create if each steppingstone is used to form a rectangle. Since 64 is a square number (8 x 8), one of the arrays would be symmetrical (a square array), which is special among all the arrays.