Shor's algorithm is a use case of factorizing in quantum computing.
The computer uses laser pulses to carry out Shor's algorithm on each atom, to correctly factor the number 15. The system is designed in such a way that more atoms and lasers can be added to build a bigger and faster quantum computer, able to factor much larger numbers.
Shor's algorithm consists of two parts: A reduction of the factoring problem to the problem of order-finding, which can be done on a classical computer. A quantum algorithm to solve the order-finding problem.
Hence Shor's algorithm is a use case of factorizing in quantum computing.
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