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There are as many definitions of cloud as there are technology bloggers. However, the major theme is that a Public Cloud provides IT resources that are provisioned remotely from the consumer and operated by a third party.
In a Private Cloud, the infrastructure policies are governed by a single organization where workloads and data can be moved to and from internal and external data centers. Private Clouds provide an organization a single point of control for security, manageability, privacy, audit, compliance and governance.
However the business case for engaging in a public or private cloud strategy involves several factors, the most important being business revenue and/or budget.