  The factorization of a large digit integer in polynomial time is a
challenging computational task to decipher. The exponential growth of
computation can be alleviated if the factorization problem is changed to an
optimization problem with the quantum computation process with the generalized
Grover's algorithm and a suitable analytic algebra. In this article, the
generalized Grover's protocol is used to amplify the amplitude of the required
states and, in turn, help in the execution of the quantum factorization of
tetra and penta primes as a proof of concept for distinct integers, including
875, 1269636549803, and 4375 using 3 and 4 qubits of IBMQ Perth (7-qubit
processor). The fidelity of quantum factorization with the IBMQ Perth qubits
was near unity.
