Is 3,564 a prime number

3,564 is not a prime number. You can automatically define this as a composite, because the number ends in an even digit. All even digits can be divided by 2, therefore 3,564 has more than 2 factors.

No. The last digit is 4, telling us that the whole thing is a multiple of 2.

Also, the sum of its digits is 18 ... divisible by 3 ... telling us that the whole thing is divisible by 3.