Difference Between Factor vs Multiple
In mathematics or arithmetic, there are different operations considered fundamental for a successful calculation and analysis. However, they might be confusing if one does not grasp each of these functions. It becomes even more challenging when two or more functions have contrasting but related operations.
Factors and multiples are mathematical terms that are essential for every arithmetical operation. They are used intermittently, but a lot of people do not know the key difference between multiple and factor. Let’s discuss further about factor vs multiple to better understand them in this thought-provoking article.
Definition of Factor
A factor is a number that gives a specific or definite result when it divides another number. In order words, it is a value that doesn’t leave any excesses when it used to divide another specific figure. For instance, 4 is a perfect factor, and one of that of 12 because it can divide 12 to give a whole number without a remainder.
Other examples when you consider that 12 includes 1, 2, 3, 4, 6, and 12. In this case, 5 cannot be a factor of 12 because when 5 divides 12, it will be equal to 2.4 or 2⅖, which are not considered as a whole number.
In a reverse form, they can be multiplied with the divided result to get back our initial amount. By and large, every number has a minimum of two factors, which are 1 and any number that is taken as the factor itself.
To determine the factors of a particular number, one simply has to get the values that evenly divide that specific number. A simple way to do that is to start dividing such numbers with 1 since 1 is a general one.
Examples: Write the factors of the following numbers
- 20 = 1, 2, 4, 5, 10, and 20
- 6 = 1, 2, 3, and 6
Definition of Multiple
A multiple is the product of two whole numbers. In clear terms, the figures that give a multiple numbers are expected to be whole numbers. For instance, 12 is a resulting multiple of 3 and 4.
Furthermore, for a specific number, it is a figure that will give a definite or whole result when it is used to divide such specific figure. The caveat is that it doesn’t give an excess or remainder in the end. Another point to note is that it doesn’t have a limit in result.
The results are indefinite or continuous. So, to calculate or determine the multiple of a given number, one needs to get the divisions of such values that can be multiplied together to give back the exact figure. Finally, for every multiple of a given number except with zero (0), there is a continuous result.
Examples: write the multiples of the following numbers
- 2 and 3 = 6
- 10 and 4 = 40
Main Differences Between Factor vs Multiple
Let us further discuss the difference between factor and multiple in the table below.
| Basis of Comparison | Factor | Multiple |
| Definition | It is a figure that gives a specific or definite outcome when it divides another figure | It is the product of two whole numbers. |
| Results | Less than or equal to such a specific figure | Greater than or equal to the given figure. |
| Numbers of Result | Limited | Unlimited or continuous |
| Operation involved | Division (÷) | Multiplication (×) |
| Illustration | If A divides B, A is factor of B | If A is divisible by B and C, A is a multiple of B and C. |
Difference Between Factor and Multiple: Conclusion
In conclusion, multiple vs factor concept is distinctive because the former uses multiplication (×) as a method of operation while latter uses division (÷). However, these two operations can be used together in a given equation or mathematical problem to get an expected outcome.
Though these two concepts are mostly taught in the elementary classes, they are inevitable in the arithmetic circus. One must be grounded in them and be sure of how they are applicable in every relevant equation. The good thing is that this guide has shown you their meanings, how to apply them, and the key discrepancies.
