Posted by **lil** on Wednesday, April 10, 2013 at 7:24pm.

how many integers, x, for which x/2, x/3 and x/5 is also an integer can be found between 1 and 500? help me!!

- algebra -
**Reiny**, Wednesday, April 10, 2013 at 8:28pm
the number must be divisible by 2, by 3, and by 5

that is it must be divisible by 30

So the sequence is

30 60 90 ... < 500

this is an arithmetic sequence, where

a = 30 and d = 30

what term is around 500

a+ (n-1)d = 500

30 + (n-1)(30) = 500

30 + 30n - 30 = 500

30n = 500

n = 16.66

so n = 16 , because 17 would be more than 500

check:

term(16) = 30 + 15(30) = 480

there are 16 such numbers

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