Final answer:
The number that can be divided into 5 and 9 equal groups without a remainder from the provided options is 180.
Step-by-step explanation:
To find a number that can be divided into 5 and 9 equal groups without a remainder, we need to find a common multiple of these two numbers. The options given are A) 75 B) 80 C) 145 D) 180. First, let's look at the multiples of 5: 5, 10, 15, 20, 25, and so forth. Then, the multiples of 9: 9, 18, 27, 36, 45, and so on. Now let's identify the lowest common multiple that appears in both lists of multiples. Option D, 180, is a multiple of both 5 (5 x 36) and 9 (9 x 20), and therefore it can be divided into 5 and 9 equal groups without leaving a remainder.