Telephone numbers are strings of digit characters, they are not integers.
Consider for example:
Expressing a telephone number in a different base would render it meaningless
Adding or multiplying two telephone numbers together, or any math operation on a phone number, is meaningless. The result is not another telephone number (except by conicidence)
Telephone numbers are intended to be entered "as-is" into a connected device.
Telephone numbers may have leading zeroes.
Manipulations of telephone numbers, such as adding an area code, are String operations.
Storing the string version of the telephone number makes this clear and unambiguous.
History: On old pulse-encoded dial systems, the code for each digit in a telephone number was sent as the same number of pulses as the digit (or 10 pulses for "0"). That may be why we still use digits to represent the parts of a phone number. See http://en.wikipedia.org/wiki/Pulse_dialing