False.
Consider 4, itself.
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4 is divisible by 2 but not by 6
138 is divisible by 6. Any number is divisible by 6 if it is an even number that also is divisible by 3.
No. 15, 25, 35, and 1675 are divisible by 5, but not by 10. However, every number divisible by 10 is also divisible by 5.
Any such number will be divisible by the even number, and therefore will also be divisible by 2.
A number that is divisible by 6 but not by 3 must be a multiple of 6 that is not a multiple of 3. Since 6 is a multiple of 3 (6 = 2 * 3), any multiple of 6 will also be a multiple of 3. Therefore, there is no number that is divisible by 6 but not by 3.