Define factor, greatest common factor, factoring and factorial


As the name implies, factors of a number are integers that divide equally into that number. It should be noted that factors are only those divisors of a number that divides the number completely without leaving a remainder behind.

For positive integers, each factor must be smaller than or equal to the original number in order for it to be considered as a factor. In other words, the numbers that could be multiplied together to generate another number are called the product’s factors or divisors. Some online factor calculator help to find the factor value accurately.

While the factor pairs are two factors that, when multiplied, are equal to the number itself. The factors are whole numbers however, for a whole number to be a factor the following rules are considered:

  • Integers are factors of the integer number itself
  • All the Integers have one common factor i.e. 1 
  • Integer factors are all less than or equal to the original number
  • For the numbers above number 1 there are always minimum 2 factors i.e. the number itself and the number 1
  • A prime number’s factors are 1 and the number itself, since prime numbers can only be multiplied by two.


It is the technique of seeking for factors in a mathematical equation to make it appear like a multiplication issue. Basically, the factoring reverses the process of multiplication or expanding an equation.

Or in other words, factoring, also known as factorization, is the process of breaking down a number into a product of many factors. When solving equations in algebra, one technique is to factor them wherever applicable.

Due to the fact that a factored expression provides us a product of expression in an equation that we may put equal to zero. 

Greatest Common Factor

GFC is the abbreviation commonly used for the term Greatest Common Factor, which is the product of prime factors that at least two or more numbers have in common. It is a method of finding the numbers and variables that are shared by a set of numbers

While doing GCF problems, in some situations, you will be asked to “factor it out,” however in some problems, you have to identify the GCF. How to find a GCF is a vital skill to learn since it should always be the initial step in the factoring process.

If you want to determine the greatest common factor (GCF), you’ll need to figure out what the prime factors are for each of the numbers you’re considering. Then you have to multiply the factors that all of the numbers have in common to get the final result of finding the GCF.


A mathematical function that is applied to all natural numbers higher than zero, is called a factorial. The factorial is represented after a number, however, an exclamation mark is used to denote the factorial function.

For instance in 6!, the ! is used to denote the factorial of number 6. To define the n factorial in mathematical terms we would say,“n! = n * (n – 1) * (n – 2) *…* 2 * 1,”. This mathematical expression refers to the product of the integers where “n” is a positive number.

Moreover, the factorial function can be defined as “n! = n * (n-1)!” which is known as the recursive definition of factorial, with the lower limit of the recursion being set at n = 2.

Despite the fact that the factorial function deals with repeated multiplication, its most apparent application in mathematics is to determine the number of different ways that a set of n items may be arranged in a given configuration.

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