No.
To be divisible by 10, the last digit must be a zero (0); 65 ends with a five (5) and thus is not divisible by 10.
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They are both divisible by 13.
1, 2, 5, 10, 13, 26, 65, 130
It is the fact that 13*5 = 65.
Yes, by these numbers: 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650.
It is divisible by 10, but not by 235.