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# Difference between factors and multiples Mathematics is a number game, where we study the numbers, their types and the concepts related to them. Arithmetic is that branch of mathematics that focuses on the properties and manipulation of numbers. Factors and multiples are two key concepts that are studied together in arithmetic, at the elementary level. A factor It is a number that leaves no remainder after it divides the specific number.

Conversely, mltiplo It is a number reached by multiplying a given number by another. While the factors of a number are finite, the multiples are infinite.

In the first instance, these two seem the same, but there are a number of differences between the factors and the multiples, which we have explained in this article.

### Comparative graph

Basis for comparison Factors Multiples
Sense Factor refers to an exact divisor of the given number. Multiple allusions to the result we get, when we multiply a given number by another number.
What is it It is a number that can be multiplied to obtain another number. It is a product obtained after multiplying the number by an integer number.
Number of factors / multiples Finite Infinite
Go out Less than or equal to the given number. Greater than or equal to the given number.
Operation Used Division Multiplication

### Definition of Factors

The term 'factors' is used to indicate the numbers that divide the number given to perfection, that is, without leaving a remainder. For example, 2 is one of the many factors of 8 since by dividing 8 by 2, we get 4 and leave no rest. The other factors of 8, which are 1, 4 and 8.

In addition, the factors are what one can multiply by another number, to obtain the required number. There are a minimum of two factors of each number, that is, 1 and the number in s.

To find out the factors of a given number, you need to identify the numbers that evenly divide that particular number. And to do so, start from number 1, as it is the factor of each number.

### Definition of multiples

In mathematics, the product of two integer numbers is defined as the multiple of the numbers. For example, 2 4 = 8, that is, 8 is a multiple of 2 and 4. In addition to this, for a given number, multiple is a number, which can be divided by exactly the given number, leaving no remainder at the end.

There is no end of multiples of a given number. Each and every number is a multiple of 0 and itself.

To find out the multiples of a given number, you need to multiply that particular number by whole numbers that start with the number 1. The resulting number, after the multiplication of the given numbers, is the multiple of a given number.

## Key differences between factors and multiples

The points given below are substantial with regard to the differences between factors and multiples:

1. The factors are described as a list of numbers, each of which completely divides a given number, that is, it is a perfect divisor of a number. On the other hand, multiples can be understood as the list of numbers that are actually the products of that particular number.
2. Factor is a number that can be multiplied by a particular number to obtain another number. On the contrary, the multiples are the product, which is achieved after multiplying the number by an integer number.
3. The number of factors of a particular number is limited, but the number of multiples of a given number is infinite.
4. The factors are less than or equal to the specific number. Unlike multiples, which are greater than or equal to the given number.
5. The operation used to obtain factors of a particular number is division. On the contrary, the operation used to obtain multiples of a number is multiplication.