The word factor is derived from the Latin word facteur, meaning a maker or doer. The first number that makes the second number, then the first number, is known as the factor of the second number. Therefore, a factor is a divisor of a number. It means the number divides the second number completely, leaving no remainder. Factors can be found using multiplication and division. In addition, they can be found by addition and subtraction, but that is a lengthy process and requires numerous iterations.
Everything around us can be factored in. For example, apples, potatoes, wall clock, etc. Factors can be a whole number or even algebraic expressions. As a result, a factor is an expression or a number that can divide any other number without leaving any remainder.
Let us take an example. We need to find a factor of 10. We know 5 x 2 = 10, or 2 x 5 = 10. We can write it; either way, the result of the product will be the same. We cannot write 10 in any other way. This means 5 and 2 are the factors of 10 because they do not leave the remainder after dividing 10. Also, they can be negative too. But they both must be negative; otherwise, -10 can be made. We can show these factors in pairs for more clarity. Therefore, the final factors of 10 are: (2, 5), (5, 2), (-2, -5) and (-5, -2).
A factor possesses the following properties:
1. The factors of a number are finite. It means there will be the same numbers that will be the factors of a particular number.
2. A factor of a number is always less than or equal to the number whose factor we need to find.
3. Every number has a minimum of two factors purposely: 1 and itself. If the number has more factors, then they are called composite numbers. If a number has only two factors, 1 and itself, they are called prime numbers.
4. Multiplication and division are the easiest and most desirable methods to find the factors of a number.
We can find the factors of a number by two methods: multiplication and division.
• Multiplication: We can find factors using multiplication operations. If we know which numbers constitute a given number, we can find the factor of the given number. In the multiplication operation, we need to write down all the factors to find all the factors.
For example, we can write 36 as:
2 x 18
3 x 12
4 x 9
6 x 6
2 x 2 x 9
2 x 2 x 3 x 3
3 x 2 x 6
4 x 3 x 3
The above factors are all possible factor pairs of 36. First, we need to find the particular pair that has numbers that cannot be further divisible. We see, 2 x 2 x 3 x 3 cannot be further divisible. Therefore, the root factors of 36 are 2 x 2 x 3 x 3.
• Division: We can find the factors of any number by the division method. In this method, we need to select the smallest number that can divide the given number to find the factors. For example, in 36, 2 is the smallest factor, and we can proceed with 2 to find all the remaining factors of 36.
We can perform the division method to find the factors as shown:
Therefore, from this, we get factors of 36 as 2 x 2 x 3 x 3. This method is also known as the prime factorization method, where we use division to find the factors of a number.