The multiplicand and multiplier are commonly referred to as factors. Factors mostly make up the dividend and divisor, or the multiplicand and multiplier, respectively.

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Factors are regarded as accurate divisors of any given number. Multiple is a term used to describe a result reached by multiplying the elements.

Multiples can be calculated when the integers are split or multiplied. The result, the product, and the numbers are primarily made up of multiples, which are divided or multiplied by factors.

## Factors vs Multiples

**The main difference between Factors and Multiples is that the multiplicand and multiplier are commonly referred to as factors. Factors usually make up the dividend and divisor, or the multiplicand and multiplier. Factors are the exact divisors of any given number. Multiples refer to a result reached by multiplying the factors. Multiples can be derived by dividing or multiplying integers. The outcome, the product, and the numbers that are divided or multiplied are all made up of multiples.**

A factor is a number that can be multiplied to get another number. The amount of factors that can be obtained by using the division method is limited in quantity or number.

The result of the factors acquired in the case of factors is either equal to or less than the specified number. The “Division” procedure is used to obtain factors.

The ancient Greek mathematician Euclid was the first to use the concept of acquiring factors.

Multiples are created by multiplying two separate numbers. Multiples are the results of multiplying two integers together.

The amount of multiples that can be obtained by multiplying is infinite in number or quantity. The outcome, product, or multiples obtained in the case of multiples are either equal to or greater than the provided number.

The operation of “multiplication” is used to obtain the product or multiples. Around four thousand years ago, the Babylonians were responsible for the introduction of the new notion of multiples.

## Comparison Table Between Factors and Multiples

Parameters of Comparison | Factors | Multiples |

Introduced by | Euclid | The Babylonians |

Meaning | Exact divisors | When two different numbers are multiplied, they give rise to Multiples |

What’s it | The number can be multiplied to obtain some other number. | Product is obtained after the process of multiplying one number with another integer. |

Quantity | Finite | Infinite |

Outcome | Equal to or less than the given number | Equal to or more than the given number |

## What are Factors?

The outcome of the factors acquired is either equal to or less than the supplied number in the case of factors. “Division” is the operation that is used to obtain factors.

A factor is a number that can be multiplied to produce another number. The amount of factors that can be obtained through the division process is limited in quantity or number.

The multiplicand and the multiplier are commonly referred to as factors. Factors primarily make up the dividend and divisor, or the multiplicand and multiplier.

For the first time, this concept of finding factors was used by Euclid, an ancient Greek mathematician. Factors are regarded as the exact divisors of any given integer.

## What are Multiples?

The operation of “multiplication” is carried out to obtain the product or multiples. Around four thousand years ago, the Babylonians were responsible for creating the new concept of multiples.

In terms of number or quantity, the number of multiples that can be obtained by performing the multiplication operation is limitless.

The outcome, product, or multiples obtained in the case of multiples is either equal to or larger than the provided number.

Multiples refer to a result that is generated by multiplying the factors. Multiples can be calculated by dividing or multiplying integers.

The product of multiplying one number by another integer is known as a multiple.

The outcome, the product, and the numbers that are divided or multiplied are mostly made up of multiples. Multiples are created when two separate numbers are multiplied.

## Main Differences Between Factors and Multiples

- Factors usually refer to the combination of the multiplicand and the multiplier. On the other hand, when the result is obtained by multiplying the factors, it is called multiples. When the integers get divided or multiplied, then multiples can be derived.
- Factors mainly constitute either dividend and the divisor or the multiplicand and the multiplier. On the other hand, multiples mainly constitute the result, the product, and the numbers through with factors are either divided or multiplied.
- Of any given number, factors are considered as the exact divisors. On the other hand, when two different numbers are multiplied, they give rise to Multiples.
- The factor is a type of number which can be multiplied to obtain some other number. On the other hand, multiples are the product that is obtained after the process of multiplying one number with another integer.
- The number of factors that can be achieved by carrying out the process of division is finite in quantity or number. On the other hand, the number of multiples that can be obtained by carrying out the procedure of multiplication is infinite in number or quantity.
- In the case of factors, the result of the factors obtained is either equal to or less than the given number. On the other hand, in the case of multiples, the result, product, or the multiples obtained is either equal to or greater than the given number.
- The operation that is carried out to obtain factors is “Division.” On the other hand, the Operation that is carried out to get the product or the multiples is done through the process of “Multiplication.”
- Euclid, the ancient Greek mathematician, was the person who used this concept of obtaining factors for the first time. On the other hand, the Babylonians are responsible for introducing the new concept of multiples around four thousand years ago.

## Conclusion

The concept of getting factors was initially applied by Euclid, an ancient Greek mathematician. Whereas, around four thousand years ago, the Babylonians were credited with inventing the notion of multiples.

A factor is a number that can be multiplied to produce a different number. The quantity or number of factors that can be obtained through the division process is limited.

Whereas, Multiples are created by multiplying two separate numbers together. The product of multiplying two integers is known as a multiple.

The outcome of the obtained factors is either equal to or less than the specified number in the case of factors. “Division” is the operation used to acquire factors.

The number or quantity of multiples that can be obtained by performing the multiplication technique is endless. The result, product, or multiples obtained is equal to or larger than the given number in the case of multiples.

The process of “multiplication” is used to obtain the product or multiples.

## References

- https://dergipark.org.tr/en/download/article-file/2173766#page=31
- https://www.tandfonline.com/doi/abs/10.1080/00207390701783264