Any four digit number where the last digit is 5 or 0 can divided through by 5.
Examples:
5455
6855
1495
1295
2365
3485
9275
1000
5230
6330
4850
9630
7410
8520
7890
4560
2320
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If the last two digits are divisible by 4 then the number is divisible by 4. Thus, if the tens digit is even and the units digit is 0 or 4 or 8 OR if the tens digit is odd and the units digit is 2 or 6 then the number is divisible by 4.
Oh, what a delightful question! The smallest 5-digit odd number is 10,001. It has five digits, and it's odd because the last digit is 1, which makes it not divisible by 2. Isn't it just a happy little number?
The smallest four digit odd integer is 1001.
ez.....9999
There are 5760 such numbers.