Daniel is organizing his rock collection of 18 rocks into equal groups. How many possible ways can Daniel line up his rock collection? Group of answer choices

5 possible ways

Explanation:

Daniel is organizing his rock collection of 18 rocks into equal groups. How many possible ways can Daniel line up his rock collection?

2 possible ways

3 possible ways

5 possible ways

6 possible ways

Solution:

Daniel has 18 rocks in his rock collection. To determine the groups in which he can organize the rocks, the factors of 18 are needed to be determined.

Factors of 18 = {1, 2, 3, 6, 9, 18}

Therefore Daniel can organize them in 1 group of 18 rocks, 2 groups of 9 rocks each, 3 groups of 6 rocks each, 6 groups of 3 rocks each, 9 groups of 2 rocks each and 18 groups of 1 rocks each.

A group must consist of 2 or more items. Therefore having 18 groups of 1 rocks each is not considered a group. The only possible ways are 5, that is 1 group of 18 rocks, 2 groups of 9 rocks each, 3 groups of 6 rocks each, 6 groups of 3 rocks each, 9 groups of 2 rocks each