Actually, yes. The most common format for storing RSA keys is PEM and it looks like this (randomly generated key just for this post):
-----BEGIN RSA PRIVATE KEY-----
MIIBOQIBAAJBAKLdFpep/qw/SIf/wsO4T17GnttlhLjLrVCfM9p4D2gnnz3OiO45
Xw1wonFOPR0D9ewAIi4yAhcMFXc2jyw3GbMCAwEAAQJAJV7R1k89jsyemgZH7J0Y
KUkuHm22/KhPxpYhUdoGvwEqvuyEFdM6kGuFj5AwMD/R8E9g1JFrQSej1aXCvHM5
oQIhANE3nxoo1pSLRrPv3/dPkq8l9VYtTcjCkiivbh6XHVa5AiEAx0gCx6DMBiGA
rxdplBG9pA91lUptz6wQbiMsFsvzfcsCIB1zD+E1yGamaDBh3ovIVqRy2mLkA6Pz
x3EUqJKDwOx5AiBW7DgaLy8O9YoV1VZ9+YcIip21MrPXQ6we/kR65RceJQIgYDV0
I5e4ncpwsbz6q+VWjZ3mNaOnNgkxESmtQY4vzQo=
-----END RSA PRIVATE KEY-----
The base64 data in the middle is a structure that contains a bunch of numbers. The numbers present in a private key are different (a supserset) of a public key, so even if it's in a format that doesn't have the BEGIN..., by parsing the structure, you can see what's in it. (Try pasting the key block above into the stdin of openssl rsa -noout -text.)