# Turing Machine divisible by 3

Turing Machine to Checks that a binary number is divisible by 3 or not?

A number is divisible by 3 if the sum of its all digits is a multiple of 3 or divisibility by 3.

*Multiple of 3: Any number that three divides evenly or any number for which 3 is a factor. For a number to be divided “evenly” by three the answer must be a whole number with no remainders. So, 30 is a multiple of 3 since 30 / 3 = 10 (10 is a whole number), but 31 is not because 31 / 3 = 10.33*

The divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

Consider a number, 204. To check whether 204 is divisible by 3 or not, take sum of the digits (i.e. 2+0+4= 6). Now check whether the sum is divisible by 3 or not. If the sum is a multiple of 3, then the original number is also divisible by 3. Here, since 6 is divisible by 3, So 204 is also divisible by 3.

Just for practiceSimilarly, if you can test that 204 is divisible for other numbers or not.

divisible by 2

Yes

divisible by 3

Yes

divisible by 4

Yes

divisible by 5

No

divisible by 6

Yes

divisible by 7

No

divisible by 8

No

divisible by 9

No

divisible by 10

No

divisible by 11

No

divisible by 12

Yes

divisible by 13

No

Turing Machine divisible by 3**Note:**

- 1->1->R and 1->R are same things. Both represent read 1, write 1, and move right.
- [ and Delta and empty cell of tape are the same things

Turing machine that checks if the input length is divisible by 3.

## Turing Machine divisible by 3 with animations

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