Given:

Number  = 7386038

Concept used:

Divisibility rule 3:

A number is divisible by 3 if the sum of the number is divisible by 3.

Sum of numbers = 7 + 3 + 8 + 6 + 0 + 3 + 8 = 35 

As, 35 is not divisible by 3

So, the number 7386038 is also divisible by 3

Divisibility rule of 9:

A number is divisible by 9 if the sum of the digits is divisible by 9 and is exactly divisible by 3.
Sum of numbers = 7 + 3 + 8 + 6 + 0 + 3 + 8 = 35

AS, 35 is not divisible by 9

So, the number 7386038 is also divisible by 9

Divisibility rule of 11:

A number is divisible by 11, if the alternating sum of the digits in the number, read from left to right. If that is divisible by 11 the number is divisible by 11.
Sum of alternating numbers

7 + 8 + 0 + 8 = 23 

3 + 6 + 3 = 12
Difference = 23 - 12 = 11
AS, 11 (i.e. difference) is divisible by 11

So, the number 7386038 is also divisible by 11

∴ The number is divisible by 11

If the number is not divisible by 3 the number is not divisible by 9

As, 3 is the factor of 9