How many bytes does the push instruction push onto the stack when I don't specify the operand size?

I can push 4 bytes onto the stack by doing this:

push DWORD 123

But I have found out that I can use push without specifying the operand size:

push 123

In this case, how many bytes does the push instruction push onto the stack? Does the number of bytes pushed depends on the operand size (so in my example it will push 1 byte)?