Project: Find the factors

Write a program that asks for a positive integer and prints every positive integer that divides it evenly, including 1 and the number itself, in ascending order. When you run it, the output should match this format:

Please enter a positive integer: 12
The factors of 12 are:
1
2
3
4
6
12

Save the file as find_factors.py.

Show a solution

Try the project on your own first. This is one working solution. Press Run, and a box asks for each input. Type the sample values from the project description to see the same output.

These tests check the solution above. They run a copy of the program, kept in PROGRAM, and give it pretend input. The testing tools here are not part of the course yet, so do not worry about how they work. Read the test names and the expected outputs: together they list what the program must do. Press Run to run the tests.

PROGRAM = r'''
number = int(input("Please enter a positive integer: "))
print("The factors of", number, "are:")
# A larger range end (such as number * 2) would also work: no number above it divides it.
for candidate in range(1, number + 1):  # pragma: no mutate
    # Using <= 0 would also work: a remainder is never negative here.
    if number % candidate == 0:  # pragma: no mutate
        print(candidate)
'''

# ---- Tests ----
import io
import sys
import unittest
from contextlib import redirect_stdout
from unittest import mock

def run_program(*typed_lines: str) -> str:
    """Run the program as if the user typed each line, and return what it printed."""
    answers = iter(typed_lines)

def fake_input(prompt: str = "") -> str:
        print(prompt, end="")
        return next(answers)

output = io.StringIO()
    with mock.patch("builtins.input", fake_input), redirect_stdout(output):
        exec(compile(PROGRAM.strip(), "solution.py", "exec"), {})
    return output.getvalue()

class TestFindFactors(unittest.TestCase):
    def assert_factors(self, number, factors):
        expected = (
            f"Please enter a positive integer: The factors of {number} are:\n"
            + "".join(f"{factor}\n" for factor in factors)
        )
        self.assertEqual(run_program(str(number)), expected)

def test_matches_the_sample_run_exactly(self):
        self.assert_factors(12, [1, 2, 3, 4, 6, 12])

def test_one_has_only_itself_as_a_factor(self):
        self.assert_factors(1, [1])

def test_a_prime_has_only_one_and_itself(self):
        self.assert_factors(13, [1, 13])

def test_two_is_the_smallest_prime(self):
        self.assert_factors(2, [1, 2])

def test_a_perfect_square_lists_its_root_once(self):
        self.assert_factors(36, [1, 2, 3, 4, 6, 9, 12, 18, 36])

def test_a_larger_number(self):
        self.assert_factors(100, [1, 2, 4, 5, 10, 20, 25, 50, 100])

def test_zero_and_negative_numbers_list_no_factors(self):
        self.assert_factors(0, [])
        self.assert_factors(-6, [])

# ---- Run the tests ----
loader = unittest.defaultTestLoader
suite = unittest.TestSuite(loader.loadTestsFromTestCase(case) for case in [TestFindFactors])
unittest.TextTestRunner(stream=sys.stdout, verbosity=2).run(suite)

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