# algebra

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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 -

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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