Factors of 10: Factor Tree, Division Method, Factor Pairs

Factors of 10 are the numbers that can be multiplied together to give the result of 10. In other words, they are the integers that evenly divide 10 without leaving any remainder. Moreover, knowing Factors helps in different practical scenarios, such as dividing items into equal groups or finding common denominators in fractions. Read on to learn more about the Factors of 10, the negative Factors, the Factor tree, the Factors of 10 by Division Method and Factor Pairs. 

What are the Factors of 10?

Factors of 10 are all the whole numbers that are divided evenly into 10 without leaving a remainder. When a number divides evenly, it means the division results in a whole number and not a fraction.

• 1 divides into 10 perfectly (10 ÷ 1 = 10)
• 2 divides into 10 perfectly (10 ÷ 2 = 5)
• 5 divides into 10 perfectly (10 ÷ 5 = 2). 

Therefore, 1, 2, 5, and 10 itself are the Factors of 10.

Also Read: Factors of 16: Negative Factors, Factor Tree, Pairs and Division Method and more! 

What are the Factors of Negative 10?

The concept of Factors applies to Negative numbers as well. Using the same principle, the Factors of negative 10 are all the whole numbers that divide evenly into -10. 

Thus, the Factors of Negative 10 are exactly the Factors of 10: -1, -2, -5, and -10.

Moreover, here is the reasoning:

• (-10) ÷ (-1) = 10 (positive divided by negative is negative)
• (-10) ÷ (-2) = 5 (positive divided by negative is negative)
• (-10) ÷ (-5) = 2 (positive divided by negative is negative)
• (-10) ÷ (-10) = 1

Hence, both positive 10 and negative 10 share the same set of factors.

Also Read: Factors of 15, Division Method, Factor Pairs and more! 

What is the Factor Tree of 10?

A Factor tree is a visual representation that shows the factorization of a number. In addition, resembles an upside-down tree, where the number you are analyzing sits at the top, and the branches show how it can be broken down into its Factors. 

Furthermore, the Factor tree for 10 will look like this:

     10

     / \

   2   5

Thus, this Tree visually shows that 10 can be factored as 2 x 5.

Also Read: Factors of 18: Factor Tree, Factor Pairs, Prime Factorization Method 

Factors of 10 by Division Method

Moreover, another method to find the Factors of 10 is through the Division Method. 

• Begin by dividing 10 by 1. Since 10 divided by 1 is 10, 1 is a factor.

• Next, continue dividing 10 by increasing whole numbers (2, 3, 4, etc.).

• If the division results in a whole number with no remainder, that number is a Factor of 10.

• You will find that 2 divides into 10 with a remainder of 0, hence making 2 a factor.

• Keep on dividing. You will discover that 5 divides into 10 with no remainder, thus proving it is a factor.

• Since 10 is already a factor by definition, and none of the next divisions will result in whole numbers (e.g., 10 divided by 3 leaves a remainder of 1), you have identified all the Factors of 10 which are 1, 2, 5, and 10. 

Also Read: Cross-Sectional Area of Different Shapes with Formula

Factors of 10 in Pairs

Additionally, the Factor Pairs for 10 are as follows:

• (1, 10)
• (2, 5)

These pairs represent two whole numbers that, when multiplied together are equal to 10. Notably, the order of the numbers in the pair does not matter as (5, 2) is also a correct way to represent the second-factor pair.

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I hope this helps! Did you like learning about the Factors of 10? You can also read on factors 1 to 25 on your compiled list here!