Factors of 105

So you need to find the factors of 105 do you? In this quick guide we'll describe what the factors of 105 are, how you find them and list out the factor pairs of 105 for you to prove the calculation works. Let's dive in!

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Factors of 105 Definition

When we talk about the factors of 105, what we really mean is all of the positive and negative integers (whole numbers) that can be evenly divided into 105. If you were to take 105 and divide it by one of its factors, the answer would be another factor of 105.

Let's look at how to find all of the factors of 105 and list them out.

How to Find the Factors of 105

We just said that a factor is a number that can be divided equally into 105. So the way you find and list all of the factors of 105 is to go through every number up to and including 105 and check which numbers result in an even quotient (which means no decimal place).

Doing this by hand for large numbers can be time consuming, but it's relatively easy for a computer program to do it. Our calculator has worked this out for you. Here are all of the factors of 105:

  • 105 ÷ 1 = 105
  • 105 ÷ 3 = 35
  • 105 ÷ 5 = 21
  • 105 ÷ 7 = 15
  • 105 ÷ 15 = 7
  • 105 ÷ 21 = 5
  • 105 ÷ 35 = 3
  • 105 ÷ 105 = 1

All of these factors can be used to divide 105 by and get a whole number. The full list of positive factors for 105 are:

1, 3, 5, 7, 15, 21, 35, and 105

Negative Factors of 105

Technically, in math you can also have negative factors of 105. If you are looking to calculate the factors of a number for homework or a test, most often the teacher or exam will be looking for specifically positive numbers.

However, we can just flip the positive numbers into negatives and those negative numbers would also be factors of 105:

-1, -3, -5, -7, -15, -21, -35, and -105

How Many Factors of 105 Are There?

As we can see from the calculations above there are a total of 8 positive factors for 105 and 8 negative factors for 105 for a total of 16 factors for the number 105.

There are 8 positive factors of 105 and 8 negative factors of 105. Wht are there negative numbers that can be a factor of 105?

Factor Pairs of 105

A factor pair is a combination of two factors which can be multiplied together to equal 105. For 105, all of the possible factor pairs are listed below:

  • 1 x 105 = 105
  • 3 x 35 = 105
  • 5 x 21 = 105
  • 7 x 15 = 105

We have also written a guide that goes into a little more detail about the factor pairs for 105 in case you are interested!

Just like before, we can also list out all of the negative factor pairs for 105:

  • -1 x -105 = 105
  • -3 x -35 = 105
  • -5 x -21 = 105
  • -7 x -15 = 105

Notice in the negative factor pairs that because we are multiplying a minus with a minus, the result is a positive number.

So there you have it. A complete guide to the factors of 105. You should now have the knowledge and skills to go out and calculate your own factors and factor pairs for any number you like.

Feel free to try the calculator below to check another number or, if you're feeling fancy, grab a pencil and paper and try and do it by hand. Just make sure to pick small numbers!

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