Yes, it is possible to delete your Azure account while keeping your Microsoft account intact.
To completely remove your Azure account:
- Go to portal.azure.com and search for "Cost Management + Billing"
- Select the subscription you want to cancel
- Click on "Cancel subscription"
Once the subscription cancelled is completed, your account will continue to exist for some time in archival mode to facilitate a reactivation of the account, if needed. After this, the archived account will be permanently deleted
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Abiola