**Factors of 21 are 1, 3, 7, 21**.

Here is complete detailed methods to find the factors of 21.

Actually, Factor is a number which divides any number completely without leaving remainder.

Or simply we can say that if we multiply two whole numbers (positive & negative) and it gives a product. Then the numbers that we multiply, are the factors of the product.

For example, if we multiply 3 to 7, it gives 21. Here 3 and 7 are called positive factors and if we multiply -1 to -21, it gives 21. So -1 and -21 are called negative factors.

Table of Contents

## How to Find The Factors of 21 ?

Since factors of 21 are the numbers, which divides 21 completely without leaving remainder. So here we are going to divide 21 by all numbers up to 21. Let’s see the process –

We have to stop the process, if any number of column ‘B’ appears in column ‘A’ or when any element comes in both columns at same level and this element will consider as a factor.

Here we stop the division when 7 appears in column ‘A’, which has already been came in column ‘B’.

Hence, all the factor of 21 in above table 1 are : 1, 3, 7, 21

Similarly, negative factor of 21 are : -1, -3, -7, -21

## What Are The Factors of 21 in Pairs ?

As we saw in above table, 1 multiply by 21 gives 21. So (1, 21) is a factor pair of 21. Let us see how many factor pairs can be achieved –

1 x 21 = 21

3 x 7 = 21

7 x 3 = 21

21 x 1 = 21

Similarly, negative factor pairs of 21 can be written as follows –

-1 x -21 = 21

-3 x -7 = 21

-21 x -1 = 21

-7 x -3 = 21

Hence, 21 has 4 factor pairs.

## What Are the Prime Factors of 21 ?

The **Prime Factors of 21 **are **2 & **7. Here we will discuss, mainly two methods of factorization to find Prime Factors of any number.

- Division Method
- Factor Tree Method

### Prime Factors of 21 by Division Method

**Step 1 :** Divide the number by the smallest prime number, which divides the number exactly.**Step 2 :** Divide the quotient again by the smallest prime number. If quotient is not exactly divisible by the

smallest prime number, choose next smallest prime number.**Step 3 :** Repeat Step 2 again and again till the quotient becomes 1.**Step 4 :** All the prime numbers used in above process are the prime factors.

Check : Multiply all the prime factors, the multiplication should be the number itself.

Caution : In this method, only prime numbers will be use to divide.

- First of all, we divide 21 by smallest prime number i.e. 2. This didn’t give a whole number as a quotient.
- Try next prime number i.e. 3. This time we got 7 as quotient and remainder is zero. (Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)
- Since 7 is a prime number, so 7 will divide by itself only.
- Here we divide 7 by 7 and we got 1 as a quotient.

Hence, 21 = 3 x 7

So **21 has two prime factor i.e. 3 & 7.**

### Factor Tree of 21

**Step 1 :** Write a number as root of the tree**Step 2 :** Find the factors of the number, each factor will be considered as root again (now, we got 2 new root)**Step 3 :** Repeat step 2 until we can’t factor any more (or until we got prime factor)**Step 4 :** The end nodes are the prime factors.

We can initiate the tree by choosing any two factors. Here we choose 3 and 7 as factors of 21.

We got the same unique nodes in every tree.

The Factor Tree may be made so many types depends upon choosing the initial and middle factors.

## Number of Factors of 21

The **Number of Factors of 21 is 4**. To find the number of factors, we use Division Method.

In our example, as we saw above 21 = 3 x 7.

**Number of factors is = (power + 1)(power + 1)(power + 1)………. **

Hence number of **factors of** 21 is = (1 + 1)(1 + 1) = 2 x 2 = 4

and if we consider both positive and negative factors, then

total no. of factors = 4 (positive) + 4 (negative) = 8

I hope, this step-by-step tutorial will be helpful to understand factorization method of 21.

## FAQ

### What are the factors or divisors of the number 21?

The factors or divisors of the number 21 are 1, 3, 7, 21.

### What are the prime factors of the number 21?

The prime factors of the number 21 are 3, 7.

### What is the total number of factors of the number 21?

The total number of factors of the number 21 is 4.

### What is the total number of prime factors of the number 21?

The total number of prime factors of the number 21 is 2.

### What is the sum of all factors of the number 21 including 21?

The sum of all the factors of the number 21 including 21 is 32 (i.e 1 + 3 + 7 + 21 = 32)

### What is the sum of all factors of the number 21 excluding 21?

The sum of all the factors of the number 21 excluding 21 is 11 (i.e 1 + 3 + 7 = 11)

### What are the factor combinations of the number 21?

The factor combinations of the number 21 are (1, 21) , (3, 7) , (7, 3) & (21, 1).

### What is the prime factorization of the number 21?

The prime factorization of the number 21 is 3, 7.

### What is the product of all factors of the number 21?

The product of all factors of number 21 is 441 (i.e. 1 x 3 x 7 x 21 = 441)

### What is the product of all prime factors of the number 21?

The product of all prime factors of number 21 is 21 (i.e. 3 x 7 = 21)

## Leave a Reply