I can, and do, remember numbers easily, and I'm not completely sure how or why. I can tell you the phone number of a house that my parents moved out of in 1976, and the post code of my high school, though I have never written to it, and left school in the 1980's. :-/
There are several ways that might help you, either break the number down into twos or threes and remember each as if a word, or a little chant 0, 2-3-4, 8-4-7, 9-2-3. Alternatively, yo may be able to remember the pattern your finger traces on the keys as you dial.
Finally, have you thought of writing down the letters from the keys and seeing if you can make a word out of them?