Abstarct: As we know, the quantum fourier transform has been investigated since 1985. the present research deals with entangled stats and superposition stats in the quantum theory and their features. And also it investigates the quick quantum fourier transform and optimization factoring speed by quantum fourier transform. the significance of the investigation and research about quantum fourier transform is because of its widely use in basic function of quantum computer. Quantum fourier transform is used in many problems of quantum computer such as; in factoring probem, order finding problem, counting solution problem, hidden subgroup problem and discrete logarithm problem. By investigating quantum fourier transform and the above mentioned points, especially factoring to prime numbers, by shor's algorithm which is the result of fourier transform, the numbers in quantum computers is factored with high speed.