At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Johanna, Jamal, Brianna, and Dyson get lockers with the numbers 300, 400, 150, and 420, respectively, who is the most popular student?
Choose the correct choice.
A) Johanna	B) Jamal	C) Brianna	D) Dyson	E) They have equal popularity
Distinct prime factors of 300 (Johanna) : 3, 2 5   Distinct prime factors of 400 (Jamal): 2 and 5.   Distinct prime factors of 150 (Brianna): 2,3, and 5   Distinct prime factors of 420 (Dyson): 2,3,5 and 7.   So most popular student - Dysonyson   Answer Dyson
<result>D</result>
At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Johanna, Jamal, Brianna, and Dyson get lockers with the numbers 300, 400, 150, and 420, respectively, who is the most popular student?