Based on choices I've seen listed elsewhere, I'd offer these as factors in bringing about African independence:
The Pan-African movement encouraged nationalism and independence for Africa.
African countries were inspired by independence movements in India and Vietnam.
European governments had been weakened by World War II.
Context/explanation:
European nations had established colonial empires in Africa in the late 19th and early 20th century. Coming out of World War II, those European nations lacked the resources and energy to maintain far-away empires in Africa and Asia -- as well as the ability to suppress independence movements that broke out in those regions after the Second World War.
It was also the case that, following the period of the World Wars, there was a prevailing attitude that people should be allowed self-determination of their nations and governments. In other words, attitudes favoring colonialism and imperialism were to be left behind, and all nations should be able to determine their own destinies.
India and Vietnam were two of the first to take on that challenge. In August, 1945, HoChi Minh led the Vietnamese people in declaring their independence from France. (Much war would follow, to accomplish that goal.) India's independence from Great Britain was declared in 1947, following a long struggle led by Mohandas Gandhi that had begun in the 1920s (and even somewhat earlier than that). India and Vietnam were examples to independence-minded people on the African continent.
According to Horace Campbell, writing for Pambazuka News (Sep. 8, 2010), "Africans who had fought against fascism in all corners of the world were also of the view that Africa should become free and independent. In October 1945, the 5th Pan African Congress was held in Manchester, UK, and the African peoples also demanded self-rule."
Pan-Africanism continued to grow stronger from their, emphasizing the need for African countries to cooperate to stand up for their strength as individual and independent nations.
The Non-Alignment Movement, to stand apart from the Cold War powers, was also a factor in strengthening African independence movements. But your question asked for three factors, not four, so I am listing that as a footnote to the list rather than the main three choices.
