# Difference between Factors and Multiples

Main difference

The main difference between Factors and Multiples is that a Factor is a number that does not go away without a remainder then divides the specific number and a Multiple is a number reached by multiplying a given number by another.

## Factors versus multiples

A factor is a count or number or quantity that divides into the target number with a remainder of zero, for example, 12 is a factor of the target number 36, because 36/12 = 3, with no remainder. A multiple is a number that is the product of a target number and an integer, for example, 36 is a multiple of the target number 12, because 12 x 3 = 36, and 3 is an integer. A factor is never greater than the target number. A multiple is never less than the target number. There is always a finite number of factors of any given objective number, as long as the objective number is not zero. So, the factors have to do with the division. There are always an infinite number of multiples of any given target number, as long as the target number is not zero. So multiples are about multiplication.

## Comparison chart

 factors multiples The factor relates to an exact divisor of the given number. Multiple relates to the result we get when we multiply a given number by another number. Number of factors / multiples Finite Infinite What is it? It is a number that can be multiplied to get another number. t is a product obtained after multiplying the number by an integer. Operation used Division Multiplication Get out Less than or equal to the given number. Greater than or equal to the given number.

## What are the factors?

Factoring in mathematics is a number or algebraic expression that divides another number or expression evenly, that is, without leaving any remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = exactly 4 and 12 ÷ 6 = exactly 2. Other factors of 12 are 1, 2, 4, and 12. A positive integer greater than 1, or an algebraic expression, that has just two factors (that is, itself and 1) is called a prime; a positive integer or algebraic expression that has more than two factors is called a composite. The prime factors of a quantity or number or an algebraic expression are the prime factors. By the basic or fundamental theorem of arithmetic, exclude, in the order in which the prime factors are written, any integer greater than one uniquely expressed as the product of its prime factors; for example, 60 written as the product 2 · 2 · 3 · 5. To determine the factors of a given number, you must identify the numbers that evenly divide that particular number. And do it, start from the number 1, since it is the factor of each number. Ways to factor large integers are of paramount importance in public key encryption, and in such methods abutting the security (or lack thereof) of data transmitted over the Internet. Factoring is also a particularly important step in solving many algebraic problems. For example, the polynomial equation Factoring is also a particularly important step in solving many algebraic problems. For example, the polynomial equation Factoring is also a particularly important step in solving many algebraic problems. For example, the polynomial equation2 – x – 2 = 0 can be factored as ( x – 2) ( x + 1) = 0.

## What are multiples?

A multiple of a number is that figure or number multiplied by an integer. Integers are both negative and positive, so other multiples of 2 are -2, -4, -6, -8, and -10. Would it be considered a multiple of 5 × 3.1? Yes, because even though 3.1 is not a whole number, it is multiplied by a whole number, so 5 × 3.1 would be considered a multiple of 3.1. To find out the multiples of a certain figure or number, you must multiply that specific number by integers starting with the number 1. The resulting number, then the multiplication of the given numbers, is the multiple of the given number. If you have ever found a common denominator for two or more fractions, you have found a common multiple. For example, if you want to add 3/8 and 5/12, you must find a common denominator. A common denominator, which is another name for the common multiple, is a number that is a multiple of all the numbers considered. For example, a common multiple for 8 and 12 is 24. This means that there is an integer 8 beat that will make 24 and there is an integer 12 beat that will make 24. Going through the 8 times tables, 8 x 3 = 24 and going over the tables of 12 beats, 12 x 2 = 24.

## Key differences

1. Factors explained as a list of numbers, each of which completely divides a given number, that is, it is a complete divisor of a number. On the other hand, multiples are understood as the list of numbers that are products of that particular number.
2. The amount or number of factors of a particular number is limited, but the number of multiples of a given number is infinite.
3. A factor is a quantity or number that can be multiplied by a particular number to get another number. On the contrary, the multiples are the product, which is reached after multiplying the number by a whole number.
4. The action used to obtain factors of a particular number is division. On the contrary, the action used to obtain multiples of a number is multiplication.
5. The factors are less than or equal to the particular number. Unlike multiples, which are greater than or equal to the given number.

## Final Thought

In conclusion, it can be said that the factors are the numbers that can be multiplied to obtain an additional number. On the contrary, the multiples are the product obtained by multiplying one number by another.