Number Divisible by 6 but not by 2 and 3

To find a number that is divisible by 6 but not by 2 and 3, we need to understand the properties of divisibility and how they apply to these numbers.

Divisibility Rules
1. A number is divisible by 2 if its last digit is even, i.e., it ends with 0, 2, 4, 6, or 8.
2. A number is divisible by 3 if the sum of its digits is divisible by 3.

Divisibility by 6
A number is divisible by 6 if it is divisible by both 2 and 3. This means the number must have an even last digit (divisible by 2) and the sum of its digits must be divisible by 3.

Example
Let's consider the number 36.

1. Divisibility by 2: The last digit of 36 is 6, which is even, so it satisfies the divisibility rule for 2.

2. Divisibility by 3: The sum of the digits of 36 is 3 + 6 = 9, which is divisible by 3. Therefore, 36 satisfies the divisibility rule for 3.

Since 36 satisfies both the divisibility rules for 2 and 3, it is divisible by 6.

Explanation
The reason why 36 is divisible by 6 but not by 2 and 3 alone is that divisibility by 6 requires satisfying both the rules for 2 and 3. If a number is divisible by 6, it must also be divisible by 2 and 3 individually.

If a number is divisible by both 2 and 3, it means the number has an even last digit and the sum of its digits is divisible by 3. In the case of 36, it has an even last digit (6) and the sum of its digits (3 + 6 = 9) is divisible by 3.

Conclusion
The number 36 is an example of a number that is divisible by 6 but not by 2 and 3 alone. By understanding the rules of divisibility and applying them, we can find numbers that satisfy specific divisibility criteria.

6=3×2. Therefore every number multiple of 6 is also a multiple of 3 or 2