'Our' is implicit. No-one is likely to exchange random numbers. One always has to use common sense!
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ReegisI met a few nice people at the festival. We exchanged telephone numbers and plan to meet again.Correct as shown. No, plurals don't require an article. "the telephone numbers" would indicate something like a list of phone numbers you had already been talking about. "our" is implied. You can add it to make it expli