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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.

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.

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 **

- 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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