Have you ever gone from needing to know what the multiples of 3 up to 100 and you have not known how to calculate them? In this article we tell you everything you need to know about these figures.
The exact sciences are always a source of uncertainty for a large part of the population, at all educational levels and even for those who have to apply knowledge about them at work. Therefore, on this occasion we want to talk about the multiples of 3 up to 100.
The multiples of 3 up to 100, and in general, they are not something that can be known by heart. Perhaps the mind can remember some, but the number of these numbers are infinite, like numerology in general.
That is why we want to provide you with the necessary information so that you can calculate, even if you need to, the multiples of 3 up to 200or any number you require, so that instead of studying it by heart, you can understand it and apply it whenever necessary.
However, before talking about the multiples of 3 up to 100it is necessary to clarify what multiple numbers are for those who do not have it completely clear, so that they can know what they are about and manage to calculate those of all the numbers that are required.
What are multiple numbers?
In principle, before calculating the multiples of 3 up to 100it is necessary to talk about what multiple numbers are, what they refer to and what must be taken into account in order to determine them, since this will help in any situation and not only with this group that we will focus on in the article.
Then,what does it mean to be a multiple of a number? As a first step, it is necessary to mention that when talking about a multiple of a number, reference is made to those that result from multiplying that number by another natural number. That is, more simply, a number X is a multiple of another number Y when X is made up of the sum of a certain number of times of Y, integer.
In turn, when mention is made of the natural numbers, are those that are used to count elements, that is, those that are not fractional or have decimals. That is, whole numbers such as: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 and so on.
For this reason, like the natural numbers are infinite multiples they will also be, since the multiples of a number, as was said before, those possible figures that arise from multiplying the number of which you want to obtain the multiples, in this case 3.
Here is an example to make the theory even clearer. Continuing with the case of this article, that is, the multiples of 3 up to 100, the number 6 is a multiple of 3. Why? Because as explained above, if a number X is a multiple of another Y when X is made up of the sum of a certain number of times of Y, it can be confirmed that 6, that is X, is a multiple of 3 (Y), because it is made up of twice 3. (3X2 =6).
How to calculate a multiple number
Considering what was said above, To calculate a multiple of any number, you must multiply that figure by the natural numbers. That is, for example, if a person wants to know the multiples of 12, he can multiply it by the natural numbers and he will obtain the multiples for him. For example 12×4= 48. So forty-eight is a multiple of 12, since it is made up of 4 times 12.
Likewise, there is another formula for calculating multiple numbers: you can find a random number and divide it by the number in question of which you want to obtain the multiple. If the division by this number results in a number without decimals, it will be a multiple, otherwise it will not.
For example, 135÷3= 45. One hundred thirty-five is a multiple of 3 since dividing it by that number gives a specific number. Otherwise, 130÷3= 43.4. In this case, hundred and thirty is not a multiple of 3, since it does not return a whole number, but rather a number with a decimal.
It is necessary to take into account that some numbers are multiples of several numbers at the same time, which does not imply an error. For example, there are common multiples for the numbers 3 and 4 such as: 0, 12, 24, 36, 48 and 60. Others can be 20, which is a common multiple of 2, 5, 10 and 20; and 40, which is a common multiple of 4, 10 and 40, to mention just a few examples.
Multiples of 3 up to 100 and 200
Now that we have already talked about what a multiple number and natural numbers refer to in order to make these concepts clear and to have a general notion of the subject, we will dedicate ourselves to what this article is about, the multiples of 3 up to 100 and the multiples of 3 up to 200.
As mentioned before, a number is a multiple of another, if it contains it a certain number of times in its entirety. That is to say that for determine the multiples of 3 up to 100, it should be considered that they are those that contain 3 a certain number of times integer.
In other words, to know if a number is multiple of 3, It must be divisible by 3, that is, it must result in a whole natural number, without decimals. As a result, it has to give a remainder of zero.
For example, if you want to know if 49 is a multiple of 3, you must perform the calculation 49÷3 = 16.33. So 49 will not be a multiple of 3, since it results in a number with decimals. Now, if the number in question is 12, it would be 12÷3= 4, in this case that number is a multiple of 3.
Now, to determine the multiples of 3, from 1 to 100, or those who want to know, there is a trick in this case. In addition to the formulas provided above, this time You can add the figures that make up the number and the sum of these numbers must give a multiple of 3.
For example, if you want to know if 27 is a multiple of 3, add the figures, that is, 2+7= 9. This result is divided by three 9/3=3, which also gives a multiple of 3. Then it can be determined that 27 corresponds to the group of multiples of 3, from 1 to 100.
Now that you have the data to calculate the multiples of any number, we will now leave the multiples of 3 from 1 to 100.
These are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72 , 75, 78, 81, 84, 87, 90, 93, 96 and 99.
Multiples of 3 up to 200
As said before, the multiples of a number can be infinite, so they do not go only up to 100 but up to the number that you want to calculate, such as, for example, the multiples of 3 up to 200.
In this sense, to calculate it, the same logic explained in the previous steps must be followed, but to facilitate the first steps, the following are also broken down: multiples of 3 up to 200but remember that you can calculate up to the number you want.
Added to the previous numbers, these are: 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162 , 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, and 201.
Now you know the multiples of 3 from 1 to 100 and up to 200 and you know how to calculate it, as well as how to find out the value of any other number you need, quickly and easily, without mistakes. The options are endless.
With these simple steps, the headaches when calculating these figures are over. And it is that, as was said, this exact science that is mathematics is not difficult, it is only necessary to know the specific formulas and understand the logic. Remember that memory will not serve here, but reasoning. To put all the knowledge into practice!
You already know the multiples of 3 up to 100 and multiples of 3 up to 200. Was the information useful to you? What other multiples do you need? Now you can avoid the headaches for this issue.
Source: A professor and Modern Mathematics