2 March 2024

In all fields of mathematics, physics and chemistry, there are aspects that are common to each other. In the case of multiples, it is that “something” that has become so fundamental that today we use it on many occasions without realizing it. It does not matter if it is in the technological aspect, that you have to apply a volumetric analysis or clearly in the labor aspect. You don’t have to be an academic to understand the operation and the application of a multiple or submultiple. However, there are still people who do not know what this is and how important it is.

So today we are going to dedicate ourselves to explaining everything you need to understand what a multiple is, how you can use it and what are the rules for its use. Likewise, you will also learn the difference between a multiple and a submultiple in case you get any kind of confusion.

Definition and meaning of a multiple

To understand the definition and meaning of a multiple of X number, two important distinctions must first be made. That is, there is two possible definitions that can be applied to this single term. On the one hand, we have the classical concept, which is:

  • The multiples are considered as those numbers or “results” that are obtained or appear once the perform a multiplication between a number by another natural. For example, if we multiply the number 3 by 2, the result of this operation is 6 or better, in other words, the multiple of three is 6.

However, there is a slightly more complex, but understandable, definition that stems from this idea of ​​multiplication. In the case of the field of physics, chemistry and advanced mathematics, multiples with base 10 are usually used for very large quantities. For example, it is easier to write 1000 km than to have to multiply this amount by 1000 more and write it. On a visual level, it may lead you to make a miscalculation.

Well, taking into account that there are multiples, what has been done in this particular case is to take 10 as the base. For example, the meter, the gram, the liter and other magnitudes are expressed in their simplest form. In the case that you want to write 1,048.576 Kb, it is more practical to write 1024 Mb or failing that, 1 Gb. All of these terms that I have used are multiples of base 10 that have been applied to the technological realm to help express larger quantities into smaller numbers. However, there are ways to identify multiples and submultiples more easily.

What is the multiple of a number?

So, in a certain way, the term multiple has two slightly different concepts, but that, in the end, they maintain a relationship. Therefore, we can summarize the definition of multiples as follows:

  • They are the results after multiplying a number X by another natural number.

  • There are multiples of do baseyes or even and odd bases.

  • In basic math, multiples are often found to the right of the equal in a math operation.

  • In the field of more advanced mathematics and linear algebra, a natural number or a medium-large number is no longer used, but multiples of base 10 are used to facilitate reading and solving a mathematical problem.

  • For each number there is a infinite amount of numberswhether even or odd, with the exception of zero.

One aspect to keep in mind is that every multiple has to be greater or less than zero, never equal. All this without forgetting that a multiple can be a positive or negative number. Therefore, this also covers the integers.

What are the rules or properties that a multiple must have?

One of the properties that every number must have is that it can be multiplied by a natural number. That is, if I want to multiply 7 by 2.5132. The result is not considered as a multiple. Therefore, it is taken only in consideration the natural numbers or integers. For this reason, the multiples of 7 are: 7, 14, 21, 28, 35… If you look closely, there is something that happens with this example, as well as with many other cases. It is that the multiples increase in quantity depending on the main number.

That is, if we are looking for the multiples of 9, these will increase by 9 units to infinity. The same thing happens with a larger number like 90, 900, etc., what will happen next is that the multiples will increase from 90 to 90 and from 900 to 900. On the other hand, an additional property that we can highlight, is that multiples can be even in odd. If you don’t know how to identify this, just look at the following:

  • Even multiples are those that end in 0, 2, 4, 6, and 8.

  • The odd ones are those that end in 1, 3, 5, 7 and 9.

In total they make a total of 10 numbers, which are the ones that represent the set of natural numbers. This can be applied to negative numbers, but as such, there would be no difference except the sign.

What is a submultiple?

As for the submultiples, these are classified as amounts that are below the base number. For example, if we take as refers to the physical magnitude of time (second), the minimum expression would be 1 second. If we apply the multiples 1 millisecond it would be equivalent to writing 1/1000. If we want to refer to 1 microsecond, this is equivalent to writing 1/1,000,000. As you will see, as the submultiple gets smaller and smaller, the smaller the seconds value becomes.

In scientific notation, the submultiple for 1 millisecond is written 1E3. What this means is that the 1 represents the base or the magnitude, the number E the base 10 and the 3, the amount of zeros that that base has. However, it can also be written much more graphically as follows: 1*10^3. Believe it or not, this can be very useful for situations where you have to take the least common multiple and provide the addition in an equation that you are solving.

What is the difference between the multiple and the divisors?

Regarding the differences between multiples and divisors, keep in mind the following key points:

  • The multiples are those that are the result of a multiplication and are infinite.

  • Every divisor is that number with base even, odd or base 10 that divides a number.

For example, if we want to find the multiples of the number 10, we would only have to multiply all the natural numbers to infinity. However, as for the divisors of the same number, they are finite. That is, that only 1, 2, and 5 would be the possible numbers. The reason for this is because when doing a division, these are the only possible results that, when proceeding with the operation, result in an exact division.

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