30 DIVIDERS list

On this occasion, from a Teacher we bring you a new math lesson that deals with what are the divisors of 30 with exercises and solutions. To do this, we will start by remembering what divisors are and how we find them, to then focus only on the divisors of the number 30. Finally, we will propose an exercise and we will leave you the solution so that you can check that you have understood it correctly.

As we have already explained in other articles in the Arithmetic category, the dividers are those numbers that divide another number exactly, that is, without the result giving decimals and without the remainder or remainder being different from zero. Thus, a number is a divisor of another if it is included in the latter a certain number of times, not infinite, and exact.

The divisors of a number they are used to know the number of groups that can be formed with a certain number and how many elements each group will be made of. In this way, it is very useful to solve problems in which we need to know the types of grouping that can be done from a natural number.

Steps to find the divisors of a number

Let's remember that for find the dividers of any number without forgetting any, the ideal and what we advise is to follow the following steps:

1. Write D (number for which we are looking for divisors) = {1, ________________, number for which we are looking for divisors}, leaving a good space in the middle.
2. Start dividing that number by 2 and, if the result is exact, write down the 2 on the right side of the 1 written in step above and the result of the division on the left side of the number from which we are looking for the divisors within the brackets.
3. Keep dividing and writing down the ones that give you the exact same way as in the previous step, with the following numbers (3, 4, 5 ...). It will end when you have to divide by the last number that you have found to the right in the brackets.

As you had already read in the title of the article, we are going to focus on the divisors of the number 30, but following the steps previously explained:

1. D (30) = {1, ______________, 30}. If you do it on paper, remember to leave a good space in the middle of both numbers, so that you can fit the other dividers.
2. We divide 30 by 2 and it gives us exactly 15, so we write it in the brackets, like this: D (30) = {1, 2, ______________ 15, 30}
3. We continue dividing by 3 and we see that it is also exact, so we write it down: D (30) = {1, 2, 3 ___________ 10, 15, 30}. We try between 4, but it does not give exact, since the result is 7.5, so we do not write it down. We try between 5 and it gives exact, so we write it down: D (30) = {1, 2, 3, 5, 6, 10, 15, 30}. As the next number that we would have to test would be 6, but we have already put it because it was the result of dividing 30 by 5, we have already finished looking for the divisors of 30.

Therefore, The divisors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

This helps us to know how many groups we can form with the number 30, for example, if they ask us if we can make 5 groups, we will know that we can. because each of them would have 6 elements, but if they asked us to make groups of 4 exactly, we could not, since 4 is not a divisor of 30.

Once you have arrived here, you have to be able to solve the following exercises. Below we leave the solutions for you to check:

1. How many groups of 3 people can we make if we are 30?
2. How many books will I put on each of the 6 shelves if I have 30 books?
3. What are the divisors of 30?

Check now that you have done the activities correctly:

1. You can make 10 groups of three people.
2. You have to put 5 books on each shelf.
3. The divisors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

If you found this lesson useful, send it to your classmates and keep browsing the tabs on our website! In the Arithmetic section you will find more articles like this one, about divisibility.