TheAlgorithms/Python · error · Exception

numbers must be integer and greater than zero

Error message

numbers must be integer and greater than zero

What it means

Raised by get_greatest_common_divisor in maths/gcd_of_n_numbers.py when any element of numbers fails factorization. The function maps get_factors over all inputs inside a try block; get_factors raises TypeError for non-positive-integers, and the except clause re-raises it as a generic Exception('numbers must be integer and greater than zero') chained from the original. One bad element aborts the whole GCD computation.

Source

Thrown at maths/gcd_of_n_numbers.py:92

        ...
    Exception: numbers must be integer and greater than zero
    >>> get_greatest_common_divisor(1.5, 2)
    Traceback (most recent call last):
        ...
    Exception: numbers must be integer and greater than zero
    >>> get_greatest_common_divisor(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
    1
    >>> get_greatest_common_divisor("1", 2, 3, 4, 5, 6, 7, 8, 9, 10)
    Traceback (most recent call last):
        ...
    Exception: numbers must be integer and greater than zero
    """

    # we just need factors, not numbers itself
    try:
        same_factors, *factors = map(get_factors, numbers)
    except TypeError as e:
        raise Exception("numbers must be integer and greater than zero") from e

    for factor in factors:
        same_factors &= factor
        # get common factor between all
        # `&` return common elements with smaller value (for Counter type)

    # now, same_factors is something like {2: 2, 3: 4} that means 2 * 2 * 3 * 3 * 3 * 3
    mult = 1
    # power each factor and multiply
    # for {2: 2, 3: 4}, it is [4, 81] and then 324
    for m in [factor**power for factor, power in same_factors.items()]:
        mult *= m
    return mult


if __name__ == "__main__":
    print(get_greatest_common_divisor(18, 45))  # 9

View on GitHub (pinned to f5988cc097)

Solutions

1. Sanitize the whole collection before calling: nums = [int(n) for n in numbers] and assert all n > 0.
2. Filter out invalid entries if they are expected noise: nums = [n for n in numbers if isinstance(n, int) and n > 0] (then require nums non-empty).
3. Catch Exception (the wrapper is generic, not TypeError) around the call if you must handle it, and inspect __cause__ for the original error.

Example fix

// before
gcd = get_greatest_common_divisor(*values)  # values may contain '1' or 0

// after
values = [int(v) for v in values]
if any(v <= 0 for v in values):
    raise ValueError(f"all inputs must be positive integers: {values}")
gcd = get_greatest_common_divisor(*values)

nums = [int(n) for n in numbers]
if not nums or any(n <= 0 for n in nums):
    raise ValueError(f"all inputs must be positive integers: {numbers!r}")
gcd = get_greatest_common_divisor(*nums)

def all_positive_ints(seq) -> bool:
    return bool(seq) and all(isinstance(n, int) and n > 0 for n in seq)

try:
    g = get_greatest_common_divisor(*nums)
except Exception as e:  # wrapper raises generic Exception, not TypeError
    if isinstance(e.__cause__, TypeError):
        # invalid element detected
        ...

When it happens

Trigger: Calling get_greatest_common_divisor('1', 2, 3) or with any single non-int, zero, or negative element among the arguments. The map(get_factors, numbers) call raises TypeError which is wrapped and re-raised.

Common situations: Spreads of mixed data (e.g. a list containing a string from parsing); forgetting that a 0 in the dataset is invalid for factorization; assuming the function skips bad values instead of failing fast.

Related errors

• Limit for the Catalan sequence must be ≥ 0
• Number should not be negative.
• Negative arguments are not supported
• the value of input must be a natural number
• abs_min() arg is an empty sequence

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/38a7ea61bb7e0e0f. Report an issue: GitHub.