What is a FACTOR in mathematics

Today we are going to prepare a new lesson from a Teacher. This lesson is about what is a factor in mathematics with examples, so we will define them and see examples. They are concepts necessary for an understanding of basic mathematics. In addition, in the end we will see some exercise and its respective solution, to verify that you have understood what has been explained.

A factor is a part of a multiplication, not counting the solution / result / product. That is, 3 and 5 are factors of 15, since 3 x 5 = 15. Actually, if you think about it, the factors are nothing more than the number divisors which is the solution. For this reason, the decomposition into factors or factorization of a number is nothing more than writing a multiplication of two or more numbers that results in that first number.

Normally, when talking about factorize, reference is made to the decomposition of number into primary numbers: 1, 3, 5, 7, 11, 13... This is the type of factorization that we are going to see in this article, since it is the most common.

Let's remember the typical phrase: "the order of the factors does not alter the product". This means that it doesn't matter if we write 4 x 2 or 2 x 4, the result is going to be 8 anyway.

Let's see how it factors from an example:

If we have to factor the number 12 into primary numbers, we'll start by checking if it can be divided exactly by two, then by three, then between 5 and so on, but only until we reach the division that results in the number 1. Let us begin:

• 12 divided by 2 is 6, so we keep the number 2 as a factor.
• 6 divided by 2 is 3, so we keep the 2 as a factor.
• 3 between 2 is not possible because it is not exact, so we look between 3 and the result is 1, so we keep 3 as a factor and we are done, because the result has already been 1.
• As can be seen, we are accumulating the result of the previous division. So the factored 12 is 2 x 2 x 3. In other words, the factors of 12 are 2 twice and 3.

Let's see it with another example of how a number is factored: let us factor into primary numbers the 1650.

• If we divide 1650 by 2, we are left with 825, so we keep the 2 as a factor.
• We continue dividing 825 by 2, but since it does not give exact, we try between 3 and it gives 275, so 3 is also a factor.
• We try 275 divided by 3 again and it's not exact, so we try between 5 and it gives 55, so 5 is a factor.
• We divide 55 by 5 and it is 11, so the 5 is again a factor.
• Now we divide 11 by 5 and it doesn't add up, by 7 either, but by 11 it does and it adds up to one, so we're done and 11 will be another factor.
• In short, 1650 can be expressed as 2 x 3 x 5 x 5 x 11.

As you will have verified, to factor you only have to know how to divide, so it is important that you refresh the multiplication tables.

We propose below that rsolve the following activities, so you can check if it is clear to you what types of angles exist and what their measurements are. At the end of the article, you can find the answers.

1. Factor the following numbers:

• 30
• 25
• 147

2. If we change the order of the factors of a multiplication, what happens to the result?

The solutions to the activities outlined above are:

1.

• 30: 2x3x5
• 25: 5x5
• 147: 3x7x7

2. If we change the order of the factors of a multiplication, what happens to the result?

Nothing happens, since the order of the factors does not alter the product.

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