HOW TO find all factors of a number?

Divide the number by every integer from 1 up to √n and pair divisors to list them efficiently.

HOW TO determine the prime factorization?

Repeatedly divide by the smallest possible prime until the remainder is 1, collecting each prime divisor.

HOW TO calculate the number of factors?

Take each exponent in the prime factorization, add 1, then multiply all resulting values together.

HOW TO use this Factor Calculator tool?

Enter a positive integer, click Calculate Factors, and review the detailed list, prime factorization, count, and sum of factors.

HOW TO find all factors of a number?

Divide the number by every integer from 1 up to √n and pair divisors to list them efficiently.

HOW TO determine the prime factorization?

Repeatedly divide by the smallest possible prime until the remainder is 1, collecting each prime divisor.

HOW TO calculate the number of factors?

Take each exponent in the prime factorization, add 1, then multiply all resulting values together.

HOW TO use this Factor Calculator tool?

Enter a positive integer, click Calculate Factors, and review the detailed list, prime factorization, count, and sum of factors.

Factor Calculator | TheCalculatorToolbox

What Is a Factor?

A factor of a number is an integer that divides that number exactly without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Understanding factors is key in simplification, number theory, and solving real-world ratio problems.

Why Factorization Matters

Prime factorization breaks a number into its prime building blocks. It’s essential for cryptography, algorithm design, solving algebraic equations, and simplifying fractions. Professionals use factorization in engineering calculations and finance models.

How This Calculator Works

Our Factor Calculator lists every divisor by iterating from 1 up to √n, pairs factors automatically, computes the prime factorization, counts how many divisors exist, and sums them—all in one step.

Step-by-Step Examples

Example 1: 36

Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36

Prime Factorization: 2² × 3²

Number of Factors: 9

Sum of Factors: 91

Example 2: 101 (prime)

Factors: 1, 101

Prime Factorization: 101¹

Number of Factors: 2

Sum of Factors: 102

Best Practices

Use prime factorization for large numbers to compute divisor count via exponents.
Check factor lists by verifying each divides evenly.
Apply factor sums in solving sigma function and divisor-sum problems.

Troubleshooting

If you enter zero, negative, or non-integer input, the calculator shows an error. Always use positive integers. Use the reset button to clear and start again.

Factor Calculator