Factors of 10—with Easy division and prime factorization

ECTI Pakistan - Factors of 10

Factors of 10

Factors of 10 are those numbers that divide the original evenly. 

The factor pairs of the number 10 are the whole numbers that, when multiplied, produce the actual number.

For example:

If we multiply 2 with 3, we get 6, which is 2 plus 3. In this case, 2 and 3 are the factors of 6. 

In the same way, we can find the factors of the given number, i.e. 10. It is also possible to determine a number’s factors using the factorization method.

Factors of 10: 1, 2, 5 and 10

In the factorization method, consider the combination of 1 and 10 as factors of 10, and then find the other multiple of 10 that gives the result as an original number. Read the following article to understand how to find factors of 10 in pairs. By using the division method, you can also find out the prime factors of 10.

What are the Factors of -10?

When we multiply two numbers and get -10 as a product, those numbers are the factors of -10. Here is the explanation:

-1 × 10 = -10

 1 × -10 = -10

 -2 × 5 = -10

 2 × -5 = -10

 -5 × 2 = -10

 5 × -2 = -10

 -10 × 1 = -10

 10 × -1 = -10

We can get -10 by having (-1, 10), (-2, 5), (-5, 2), and (-10, 1) as a pair of factors. Similarly, we can also get -10 by having(1, -10), (2, -5), (5, -2), and (10, -1) as a pair of factors.

How to Find the Factors of 10?

You can find factors of 10 by following the steps below.

Step 1: 

Start by writing the number 10.

Step 2: 

Find two numbers that result in 10 when multiplied, for example, 2 and 5, so that 2 × 5 = 10.

Step 3: 

As we know, 2 and 5 are prime numbers with only two factors, namely one and the number itself. 

The factors of 2 = 2 × 1

The factors of 5 = 5 × 1

Therefore, they can’t be further factorized.

Step 4: 

As a result, the factorization of 10 can be expressed as 10 = 2 × 5 × 1

Step 5: 

In the end, list all the unique numbers we can obtain from the above process.

Factors of 10
1, 2, 5, and 10

Pair Factors of 10

In order to find the pair factors of 10, multiply the two numbers together in order to get the original number as 10. Here are the pair factors for both positive and negative integers:

Positive pairsNegative pairs
1 × 10 = 10; (1, 10)(-1) × (-10) = 10; (-1, -10)
2 × 5 = 10; (2, 5)(-2) × (-5) = 10; (-2, -5)
5 × 2 = 10; (5, 2)(-5) × (-2) = 10; (-5, -2)
10 × 1 = 10; (10, 1)(-10) × (-1) = 10; (-10, -1)

So, the positive pair factors of 10 are (1, 10), (2, 5), (5, 2), and (10, 1).

And also the negative pair factors of 10 are (-1, -10), (-2, -5), (-5, -2) and (-10, -1).

Prime Factors of 10

In fact, 10 is a composite number that includes prime factors. Now let’s identify 10’s prime factors.

ECTI Pakistan - Factors of 10
  • As a first step, divide the number 10 by the smallest prime number, i.e. 2.

10 ÷ 2 = 5

Dividing 5 by 2 is now easy.

5 ÷ 2 = 2.5

The factor of 5 cannot be 2, because whole numbers should be used as factors. Hence, we should proceed to prime numbers 3, 5, and 7

5 ÷ 3 = 1.6667

5 ÷ 5 = 1

  • In the division process, we received number 1, which means we are unable to move forward. 

Therefore, the prime factors of 10 are 2 and 5, where 2 and 5 are the prime numbers.

The prime factorization of 10 is 2 × 5.

Tips and tricks

The following are some important facts about the factors of 10:

The number of factors of 10 is four.

The sum of all the factors of 10 equals 18.

All the factors of 10 add up to 10 times the square of 10 or 10 times the product of the factors of 10.

Get Factors of More Numbers Here

Factors of eleven= 1 and 11.Factors of 15= 1, 3, 5, and 15.Factors of 16= 1, 2, 4, 8 and 16.
Factors of 17= 1 and 17.Factors of 18= 1, 2, 3, 6, 9, and 18.Factors of 20= 1, 2, 4, 5, 10, and 20.
Factors of 21= 1, 3, 7, 21.Factors of 23= 1, 23.Factors of twenty four= 1, 2, 3, 4, 6, 8, 12, and 24.
Factors of 25= 1, 5, and 25. Factors of sixty two= 1, 2, 31, and 62.Factors of 28=  1, 2, 4, 7, 14 and 28.

FAQs

What are all the multiples of 10?

The multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, etc.,

What are the prime factors of 10?

Prime factors of 10 = 2 and 5.

What are the factors of a number?

Factors are numbers multiplied together to make another number. A number may have two or more factors.

What are all factors of 12?

Factors of 12 are 1, 2, 3, 4, 6, and 12.

What are the factors of 100?

Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

How many factors do 10 and 100 have?

There are four factors in the number 10, including 1, 2, 5, and 10.
There are 9 factors in the number 100, such as 1, 2, 4, 5, 10, 20, 25, 50, and 100.