Table of Contents

### Main Difference

The main difference between Factors and Multiples is that a Factor is a number that departs no remainder behind then it divides the specific number and Multiple is a number reached by multiplying a given number by another.

### Factors vs. Multiples

A factor is a count or number or quantity that divides into the target number with a remainder of zero, e.g., 12 is a factor of the target number 36, because of 36/12 = 3, with no remainder. A multiple is a number that is a product of a target number, and an integer, e.g., 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 target number, so long as the target number is not zero. So factors are about division. There is always an infinite number of multiples of any given target number, so long as the target number is not zero. So multiples are about multiplication.

### Comparison Chart

### What are the Factors?

Factor in math is a number or algebraic expression that splits other number or expression evenly—i.e., with no remaining. E.g, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. Others factors of 12 are 1, 2, 4, and 12. A positive integer larger than 1, or an algebraic expression, that has simply two factors (i.e., itself and 1) is called prime; a positive integer or an algebraic expression that has beyond than two factors is called composite. The prime factors of a quantity or number or an algebraic expression are those factors which are prim. By the basic or fundamental theorem of arithmetic, exclude for the order wherein the prime factors are written, every whole number larger than one uniquely expressed as the product of its prime factors; for example, 60 written as the product 2·2·3·5. To ascertain factors of a given number, you need to identify the numbers that evenly divide that particular number. And do so, start right from number 1, as it is the factor of every number. Ways for factoring large whole numbers are of utmost importance in public-key encryption, and on such methods abutting the security (or lack thereof) of data transmitted over the Internet. Factoring is also a particularly important step in the solution of many algebraic problems. For example, the polynomial equation *x*^{2} − *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 negative as well as positive, so other multiples of 2 are -2, -4, -6, -8 and -10. Would 5×3.1 be considered a multiple? Yes, because even though 3.1 is not an integer, it is multiplied by an integer so 5×3.1 would be considered a multiple of 3.1. To find out multiples of a given figure or number, you need to multiply that specific number by integers start with number 1. The resultant number, later the multiplication of the provided 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 common multiple, is a number that is a multiple for all the numbers considered. For example, a common multiple for 8 and 12 is 24. This means that there is an integer time 8 that will make 24 and there is an integer time 12 that will make 24. Going through the 8-time tables, 8 x 3 = 24 and going through the 12-time tables, 12 x 2 = 24.

### Key Differences

- Factors explained as a list of numbers, each of which, entirely divides a given number, i.e., it is a complete divisor of a number. On the other hand, multiples understood as the list of numbers which are the products of that particular number.
- The quantity or number of factors of a particular number is limited, but the number of multiples of a given number is endless.
- A factor is a quantity or number that can be multiplied with a particular number to obtain another number. Conversely, multiples are the product, which reached after multiplying the number by an integer.
- The action used for obtaining factors of a particular number is division. As opposed, the action used for getting multiples of a number is multiplication.
- Factors are whether less than or equal to the particular number. Unlike multiples, which are larger than or equal to the given number.

### Conclusion

In conclusion, it can be said that factors are the numbers that can be multiplied to get a further number. On the contrary, multiples are the product, that one can get by multiplying a number with another.