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FIND THE SMALLEST POSITIVE NUMBER THAT IS

DIVISIBLE BY 15 AND HAS ONLY
0 AND 1 AS DIGITS (E.G. 10, 11, 100...)

User Gudrun
by
7.5k points

1 Answer

5 votes

Answer:

1110

Explanation:

For a number to be a divisible of 15 it has to end in either the digit 5 or the digit 0

It also has to be divisible by both 5 and 3 which are primes

Remember that for a number to be divisible by 3, the sum of the digits must be a multiple of 3. For example 27 is divisible by 3(2+7 9 which is a multiple of 3)

We can ignore 2 digit numbers since we only have one possibility 10

  • With these facts lets start with 3 digit numbers and having digits 1 and 0 only, ending in 0, divisible by 3. We get:
    100 and 110 are the only possible 3-dgit numbers. Neither is divisible by 3
  • Let's go to 4-digit numbers. We get
    1000, 1010, 1100, 1110. The only number divisible by 3 is 1110

So the answer is 1110

User Everspader
by
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