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What is the sum of factors of 21 ?

To find the sum of factors of 21 first we have to find the factors of 21 .

Factors of 21 are those integers that can divide 21 evenly into equal parts.

Factors of a number include those numbers at which that number is divisible. The concept can be more cleared from the following points:

  • The factor of 21 is that number that will divide 21 completely i.e. where the remainder is zero.
  • The number 21 is composite. Composite numbers are those numbers that have more than two factors.
  • The factors of 21 are all the integers that divide 21 without any remainder.

According to the definition the factors of 21 are 1, 3, 7 and 21 because these are the numbers that divides 21 without any remainder.  Let’s understand how to calculate them.

How to calculate the factors of 21?

By following the below mentioned steps we can find the factors of 21.

Step 1: First , write the number 21

Step 2: Find the two numbers which results in 21  after multiplying them  like 3 and 7 , such that 3 * 7 = 21

Step 3: We know that 3 and 7 are prime numbers with only two factors  that is one and the number itself .

The factors of 3 = 3 * 1

The factors of 7 = 7 * 1

So, we cannot further factorize them.

Step 4: Therefore the factorization of 21 can be expressed as 21 = 3 * 7 * 1

Step 5: Finally, write down all the unique numbers which we can obtain from the above process.

Hence the factors of 21 are 1, 3, 7 and 21.

Pair Factors of 21

To find the pair factors of 21, we need to group them in such as a way that when we multiply the two we get 21.

Positive Pairs

Positive pairs of 21 can be written as  :

( 1 , 21 )  ,  ( 3 , 7 )  ,  ( 7 , 3 )  , ( 21 , 1 )

Negative Pairs

Negative pairs of 21 can be written as :

( – 1 , -21 )  , ( – 3 , – 7 )  , ( -7 , – 3 )  ,   ( – 21 , – 1 )

Out of the factors of 21   numbers 3 and 7 are prime numbers.

Another way of finding factors: Prime Factorization of 21

A prime factorization is the result of factoring a number into a set of components of which every member is a prime number.  This is generally written by showing 21 as a product of its prime factors. For 21, this result would be:

21 = 3 * 7 * 1

Also, 1 and the number itself are the factors of every number.

So, from above discussion we can say that the number 21 has 4  factors : 1 , 3 , 7 , 21

In above factors 1 is the smallest and 21 is the largest factor.

Now, we have all the factors of 21. Let’s find their sum.

Sum of factors of 21

Factors of 21 = 1, 3, 7 and 21

Sum of factors of 21 = 1 + 3 + 7 + 21 =  32

Hence, the sum of factors of 21 is  32

Some interesting insights

  • The number of prime factors of 21 is 10 (as only 3 & 7 are prime and 1 is neither prime nor composite).
  • The sum of all factors of 21 is 32 .
  • The product of all factors of 21 is equal to square of 21 or 21 times of 21.

Product of all factors = 1 x 3 x 7 x 21 = 21 x 21 =  = 441

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