Final answer:
The greatest distance Ben can place the fence posts apart around his 24 feet by 56 feet garden is 8 feet, as it is the greatest common divisor for both dimensions, allowing for even spacing.
Step-by-step explanation:
Ben's garden is 24 feet long and 56 feet wide, and he wishes to place fence posts the same distance apart along all sides. To find the greatest distance apart that he can place the fence posts, we need to determine a common divisor for both the length and the width of the garden. The largest common divisor will give us the maximum spacing between the fence posts that can be used uniformly on all sides.
Both 24 and 56 are divisible by 8, which is their greatest common divisor (GCD). Therefore, the largest distance that Ben can place the fence posts apart while ensuring they are spaced equally on all sides is 8 feet. If we were to choose a larger spacing, the consistency of the spacing along each side would not be possible.