Hi, thanks for taking the time to answer my question!

Which of the following sets contain only factors of the number 75?

(A) {1,4,5,20}
(B) {1,3,5,25}
(C) {0,75,100,125}
(D} {3,15,17,25}
(E) {2,3,5,15}

Please explain how you did it as well, thank you 🙂

A factor of x is a number than evenly divides x. So 3 is a factor of 75, because 75/3 = 25, which is an integer. 10 is NOT a factor of 75, because 75/10 = 7.5, which is NOT an integer.

The best way to go for this question is just to list the factors of 75, which you do by dividing it by a bunch of things until you start getting repeats. First divide it by 1 (1 is a factor of everything). Then divide it by 2 (which won’t work, in this case). Then divide by 3, etc. The list of factors you should come up with:

1, 75
3, 25
5, 15

Once you divide by 5, if you keep going you won’t get another factor until you get to 15. Since you already had 15 from when you divided by 5, you know you’re done and have listed all the factors of 75.

Now look at your answer choices. Only choice B has numbers from the list we generated and no other numbers.