Factor Calculator | Best Calculator

Factor Calculator

Calculated Factors:
Formula:
Factors are the numbers that divide a given number exactly.
Example:
If 12 is entered:
Factors: 1, 2, 3, 4, 6, 12
Copied!

Understanding Factors

A factor is a number that divides another number evenly, without leaving a remainder. For example, in the equation 6 × 5 = 30, both 6 and 5 are factors of 30. Other factors of 30 include 1, 2, 3, 10, 15, and 30. In general, if a number a can divide another number b with no remainder, then a is a factor of b. Factors play an important role in simplifying fractions and identifying numerical patterns.

What Is Prime Factorization?

Prime factorization means expressing a number as a product of its prime factors—prime numbers that multiply to give the original number. For instance, the prime factorization of 120 is:

2 × 2 × 2 × 3 × 5

One common method for finding prime factors is using a factor tree, which breaks a number into smaller parts until only prime numbers remain.

Example – Factor Tree of 120:

            120
            / \
          2 60
            / \
          2 30
             / \
            2 15
              / \
             3 5

So, the prime factors of 120 are 2 × 2 × 2 × 3 × 5.

Why Prime Factorization Matters

Finding prime factors is simple for small numbers, but it gets much harder with large numbers. For example, RSA-768, a 232-digit number, took hundreds of computers and two years to factor by a team of researchers. Because of the complexity, most online calculators (like this one) handle numbers up to a reasonable size.

Even though no fast algorithm exists for factoring extremely large numbers, the search is ongoing. A discovery of such a method—or a proof that one cannot exist—would be a major achievement in mathematics.

 

Mathematics Calculators