The United Kingdom of Great Britain does not exist, Great
Britain is England, Scotland and Wales. The United Kingdom is Great
Britain and Northern Ireland.
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Great Britain is formed from England, Scotland and Wales.
The United Kingdom is Great Britain and Northern Ireland.
So the answer is YES, Great Britain is part of the UK.
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The Kingdom of Ireland and the Kingdom of Great Britain were
united to form the United Kingdom of Great Britain and Ireland with
the passing of the Acts of Union 1800. In this way, the United
Kingdom became a single kingdom.
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United Kingdom of Great Britain and Northern Ireland.