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Python Program to Find the Factors of a Number

Beginner · Numbers

A factor of a number divides it exactly, with no remainder: the factors of 12 are 1, 2, 3, 4, 6 and 12. This program finds all the factors of a number by testing every number from 1 up to it.

Program

factors_of_a_number.py
num = 36 # or: num = int(input("Enter a positive number: "))
factors = []
for i in range(1, num + 1):
if num % i == 0: # no remainder, so i is a factor
factors.append(i)
print(f"Factors of {num}: {factors}")
print("Number of factors:", len(factors))
print("Sum of factors:", sum(factors))
Output
Factors of 36: [1, 2, 3, 4, 6, 9, 12, 18, 36]
Number of factors: 9
Sum of factors: 91

How it works

  1. The loop tries every number i from 1 to num.
  2. num % i is the remainder after dividing, so num % i == 0 means i divides num exactly.
  3. Each factor found is added to the factors list.
  4. len() counts the factors and sum() adds them up; 36 has 9 factors because it is a perfect square, and its middle factor 6 pairs with itself.

Other ways to write it

Faster: check up to the square root

Faster: check up to the square root
num = 36
factors = []
i = 1
while i * i <= num:
if num % i == 0:
factors.append(i)
if i != num // i: # 6 x 6: do not add 6 twice
factors.append(num // i)
i += 1
print(f"Factors of {num}: {sorted(factors)}")
Output
Factors of 36: [1, 2, 3, 4, 6, 9, 12, 18, 36]

Factors come in pairs, like 4 x 9 = 36, so finding the small one gives the big one too. Stopping at the square root makes this far faster for large numbers.

Using a list comprehension

Using a list comprehension
num = 100
factors = [i for i in range(1, num + 1) if num % i == 0]
print(f"Factors of {num}: {factors}")
Output
Factors of 100: [1, 2, 4, 5, 10, 20, 25, 50, 100]

A list comprehension builds the same list of factors in a single line.

Try it yourself

Use the number of factors to print whether the number is prime: a prime has exactly 2 factors.

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