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Re: At a certain high school, a student’s popularity is determined by his
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15 Apr 2016, 06:48
Since they each end in 0, they each have 10 as a multiple, so each number will include 2 and 5 as common prime factors.
300 = 30*10. prime factors of 10 is 2, 5
400 = 40*10. prime factors of 10 is 2, 5
150 = 15*10. prime factors of 10 is 2, 5
420 = 42*10. prime factors of 10 is 2, 5
Divide each number by 10, and this leaves you with smaller, simpler numbers to figure out the rest of the equation (30, 40, 15, 42)
Again 30 and 40 are divisible by 10, so we immediately know that we haven't added any new prime factors there. so that leaves us with
3
4
15
42
so far, all number share the same 2 unique prime factors (2 and 5), so we can now break out the remaining Prime factors as follows:
3 = 3 (one new prime number)
4 = 2, 2 (nothing new here)
15 = 3, 5 (one new prime number)
42 = 2, 3, 7 (TWO new prime numbers)
This means that 420 has the most unique prime numbers, and is therefore the correct answer. (D: Dyson)