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Factoring Calculator

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How to Factor Numbers: Factorization

This factors calculator factors numbers by trial division. Follow these steps to use trial division to find the factors of a number.

  1. Find the square root of the integer number n and round up to the next whole number. Let’s call this number s .
  2. Start with the number 1 and find the corresponding factor pair: n 1 = n. So 1 and n are a factor pair because division results in a whole number with zero remainder.
  3. Do the same with the number 2 and proceed testing all integers (n 2, n 3, n 4. n s ) up through the square root rounded to s. Record the factor pairs where division results in whole integer numbers with zero remainders.
  4. When you reach n s and you have recorded all factor pairs you have successfully factored the number n .

Example Factorization Using Trial Division

  • The square root of 18 is 4.2426, rounded up to the next whole number is 5
  • Testing the integer values 1 through 5 for division into 18 we get these factor pairs: (1 and 18), (2 and 9), (3 and 6). The factors of 18 are 1, 2, 3, 6, 9, 18.

Factors of Negative Numbers

All of the above information and methods apply to factoring negative numbers. Just be sure to follow the rules of multiplying and dividing negative numbers to find all factors of negative numbers. For example, the factors of -6 are (1, -6), (-1, 6), (2, -3), (-2, 3). See the Math Equation Solver Calculator and the section on Rules for Multiplication Operations .

Related Factoring Calculators

See our Common Factors Calculator to find all factors of a set of numbers and learn which are the common factors.

The Greatest Common Factor Calculator finds the greatest common factor (GCF) or greatest common divisor (GCD) of a set of numbers.

See the Least Common Denominator Calculator to find the lowest common denominator for fractions, integers and mixed numbers.