1. First sign in to Yahoo Messenger
2. At the top click on Messenger and select Privacy Options
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3. In the left hand side panel, at the top, click on General
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4. Now in the right hand side panel, at the bottom, click on Edit Mobile Phone or simply hit P from your keyboard
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Note : If you do not have Yahoo Messenger follow this link and sign into your Yahoo account
5. After visiting Yahoo Mobile page, click on Edit at the right hand side.
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6. If you want to completely remove your mobile number, clear the text box and select Change and if you to change your number, enter the new number and click on Change
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7. Another way to completely remove your mobile number is to select the Delete option on the first Yahoo Mobile page