What is the smallest number consisting of Zero's & one's that is divisible by 15???

Question

1111 is wrong it should be in decimal

Answer 1

{ 10 , 11 }
{ 100 , 101 , 110 , 111 }
{ 1000 , 1001 , 1010 , 1011 , 1100 , 1101 , 1110 , 1111 }

just ' 1110 / 15 = 74 ( decimal ) '

Good Luck

Answer 2

15 = 3 * 5
Any number multiplied by 5 ends in a 0 or 5. your final number can't have a 5 so it will end in 0.
A number ending in 0 is even and has 2 as a factor
15 doesn't have 2 as a factor so the number it is multiplied by must be 2 times something.
3 * 5 * (2 * something) =
3 * 10 * something
A number divisible by 3 has digits that add up to a multiple of 3.
Since you can only use the digits 1 and 0, 111 is the way to add up 3 with the least number of digits. using a 0 just makes the number bigger. Your last digit has to be zero so combining these gives 1110 as your answer

Answer 3

A number that is divisible by 15 must be divisible by 3 and by 5.
Fact 1: A number is divisible by 3 if the sum of its digits is divisible by 3.

Fact 2: A number is divisible by 5 if its one's digit is either 0 or 5.

Now since the number must only consist of zeros and ones, it followos from Fact 2 that the one's digit of "our number" must
be 0.

Any two digit number or three digit number consisting of ones AND zeros will not be divisble by 3 because the sum of its digit will not divide 3.

Below is a list of four digit numbers consisting of 0's and 1's:
1000, 1001, 1010, 1100, 1101, 1110, ...

The first 5 numbers in the list are not divisible by 15, because none of them satisfies facts 1 and 2. However, 1110 does, and thus it is the smallest desired number with that property.

Answer 4

Your number must be divisible by 3 and 5. To be divisible
by 5 it must end in 0. To be divisible by 3 it must have
at least 3 ones. The smallest number meeting
these criteria is 1110.

Answer 5

6

Answer 6

1111 in Binary - very clever, man.

In the decimal system of everyday life, it would be 1, because you never specified that it had to be evenly divisible by 15, only that it had to be divisble in some way or another. So, 1, whick would make 0.06666>>>

Answer 7

1110

The number has to end in 0, not 1, since it has to be divisible by 5. Also has to have three 1's, since it's divisible by 3. Smallest number meeting these criteria is 1110.

Answer 8

1110

Answer 9

How about 1110

Answer 10

1110