Hints and solutions to Look for a pattern #7
How many numbers less than 124 are divisible by 2, 3 and 5?
- Well, since 2 x 62 = 124, there are 62 multiples of 2.
And 124 = 3 x 41 + 1, so there are 41 multiples of 3 less than 124,
and 124 = 5 x 24 + 4, so there are 24 multiples of 5 less than 124.
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But it might be easier to think about which numbers are multiples of
all three of 2, 3 and 5. (To do a simpler one, you might consider which
numbers are multiples of both 2 and 3, or 2 and 5, or 3 and 5).
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If a number is divisible by all three of 2, 3, and 5, then it must be
divisible by their product (since they are all prime numbers). Thus,
it is the multiples of 2 x 3 x 5 = 30 that are divisible by all three.
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And there are 4 multiples of 30 less than 124, so the answer to this
question
is 4.