Introduction
In this tutorial we will go through Shor’s Algorithm and see how to run it on IBM’s quantum computers with Python and Qiskit.
What is the Shor’s Algorithm
Shor’s Algorithm is a quantum algorithm for integer factorisation. Simply put given an odd integer N it will find it’s prime factors.
The algorithm consists of 2 parts:

Classical part which reduces the factorisation to a problem of finding the period of the function. This is done classically using a quantum computer

Quantum part which uses a quantum computer to find the period using the Quantum Fourier Transform.
For the algorithm the steps are as follows:

Pick a random number A such that A < N

Computer the greatest common divisor (GCD) of and N

if the gcd != 1 then we found a factor of N

If not then run the quantum circuit that uses a Quantum Fourier Transform

If the period is odd then go back to step 1

Otherwise we have found the factors of N
Implementation
The algorithm can be implemented incredibly easily since Qiskit has a baked in function for the algorithm called Shor(N).
Where N will be the integer you wish to factor. For example Shor(21) will find the prime factors for 21.
Note: For this tutorial you will need an API token which you can get by registering here: https://quantumcomputing.ibm.com/
Code
from qiskit import IBMQ
from qiskit.aqua import QuantumInstance
from qiskit.aqua.algorithms import Shor
IBMQ.enable_account('ENTER API TOKEN HERE') # Enter your API token here
provider = IBMQ.get_provider(hub='ibmq')
backend = provider.get_backend('ibmq_qasm_simulator') # Specifies the quantum device
print('\n Shors Algorithm')
print('')
print('\nExecuting...\n')
factors = Shor(21) #Function to run Shor's algorithm where 21 is the integer to be factored
result_dict = factors.run(QuantumInstance(backend, shots=1, skip_qobj_validation=False))
result = result_dict['factors'] # Get factors from results
print(result)
print('\nPress any key to close')
input()
Output
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