Hello! I know this is not the usual type of post, but I need some help for an SAT type math question for a student I tutor. I was hoping that some of the Math teachers on here would help me, since I really can't figure out what is wrong with the student's solution. Here's the problem: Andrew has 50 small boxes, 60 medium size boxes, and 70 large size boxes. He wants to arrange them in rows so that there are equal number of same size boxes in each row. How many rows will he need, to be able to arrange the boxes? (A) 10 (B) 12 (C) 15 (D) 18 (E) 70 Here's the solution from the tutoring company: To find the number of rows so that there are equal number of boxes of the same size in each row, the total number of boxes must be divided with the greatest common factor (GCF) of the number of boxes of each size. The prime factorization of 50 = 2 5 The prime factorization of 60 = 2 2 3 5 The prime factorization of 70 = 2 5 7 Thus, the GCF of 50, 60, and 70 = 10 The number of rows of boxes = (50+60+70) /10 = 180 180/10 = 18 The correct answer is (D). Now, my student said he could take 5 small, 6 medium, and 7 large per row- which means 18 boxes per row, for 10 rows- rather than the company's solution of 18 rows with 10 boxes each. I really do not get what is wrong with his solution of A. Maybe I'm looking at it wrong, but I really cannot figure this one out. Please help!