Factor Calculator.

In mathematics, a factor is a whole number that divides another number exactly, leaving no remainder. Factors play a key role in multiplication, division, fractions, and number patterns.

For example, when we multiply 6 × 5 = 30, both 6 and 5 are called factors of 30. In fact, any number that can divide 30 evenly is also a factor.

In simple terms, a number a is a factor of another number b if b ÷ a results in a whole number without any remainder.

Factors are extremely useful in mathematics. They help in:

• Simplifying fractions
• Finding greatest common divisors (GCD)
• Understanding number patterns
• Solving algebraic expressions

Prime factorization is the process of breaking a number down into prime numbers that multiply together to give the original number. Prime numbers are numbers greater than 1 that have only two factors: 1 and themselves.

For example, the prime factorization of 120 is:

One of the easiest ways to find prime factors is by using a factor tree, which visually breaks a number into smaller factors until only prime numbers remain.

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

While prime factorization is simple for small numbers, it becomes increasingly difficult as numbers grow larger. Currently, there is no known fast algorithm that can efficiently factor extremely large numbers.

A famous example is RSA-768, a 232-digit number that took researchers nearly two years and hundreds of computers to factor completely.

Even though no efficient universal method exists today, mathematicians have not proven that such an algorithm is impossible—leaving the door open for future discoveries.

Understanding factors and prime factorization builds a strong foundation in mathematics. These concepts are essential not only for basic arithmetic but also for advanced topics like cryptography, algebra, and number theory.

Whether you are simplifying fractions or exploring complex mathematical problems, factors remain one of the most important tools in math.