# Factors of 21

Factors of 21 are 1, 3, 7, and 21

#### How to find factors of a number

 1.   Find factors of 21 using Division Method 2.   Find factors of 21 using Prime Factorization 3.   Find factors of 21 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 21

• Divide 21 by 1: 21 ÷ 1 : Remainder = 0
• Divide 21 by 3: 21 ÷ 3 : Remainder = 0
• Divide 21 by 7: 21 ÷ 7 : Remainder = 0
• Divide 21 by 21: 21 ÷ 21 : Remainder = 0

Hence, Factors of 21 are 1, 3, 7, and 21

#### 2. Steps to find factors of 21 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 21 using the division method, follow these steps:

• Step 1. Start dividing 21 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 21, which is 3. Divide 21 by 3 to obtain the quotient (7).
21 ÷ 3 = 7
• Step 3. Repeat step 1 with the obtained quotient (7).
7 ÷ 7 = 1

So, the prime factorization of 21 is, 21 = 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 21 as shown below:

So, the prime factorization of 21 is, 21 = 3 x 7.

#### 3. Find factors of 21 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 21 would be the two numbers which, when multiplied, give 21 as the result.

The following table represents the calculation of factors of 21 in pairs:

Factor Pair Pair Factorization
1 and 21 1 x 21 = 21
3 and 7 3 x 7 = 21

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 21. They are called negative pair factors.

Hence, the negative pairs of 21 would be ( -1 , -21 ) , ( -3 , -7 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 7, 21 are exact divisors of 21.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 21 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 21.

• What are the prime factors of 21?

The factors of 21 are 1, 3, 7, 21.
Prime factors of 21 are 3, 7.

• What two numbers make 21?

Two numbers that make 21 are 3 and 7.

• What is the greatest prime factors of 21?

The greatest prime factor of 21 is 7.

• What are factors of 21?

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

• How do you find factors of a negative number? ( eg. -21 )?

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

• What are five multiples of 21?

First five multiples of 21 are 42, 63, 84, 105, 126.

• Write some multiples of 21?

First five multiples of 21 are 42, 63, 84, 105.

• Is 21 a perfect square?

No 21 is not a perfect square.

• What two numbers make 21?

Two numbers that make 21 are 3 and 7.

#### Examples of Factors

What is prime factorization of 21?

Prime factorization of 21 is 3 x 7 = 3 x 7.

Sammy is puzzled while calculating the prime factors of 21. Can you help him find them?

Factors of 21 are 1, 3, 7, 21.
Prime factors of 21 are 3, 7

Kevin has been asked to write 3 factor(s) of 21. Can you predict the answer?

3 factor(s) of 21 are 1, 3, 7.

Joey wants to write all the prime factors of 21 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 21 are 3, 7.
So in exponential form it can be written as 3 x 7.

How many factors are there for 21?

Factors of 21 are 1, 3, 7, 21.
So there are in total 4 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 21? Help her in writing all the factors.

Positive factors are 1, 3, 7, 21.
Negative factors are -1, -3, -7, -21.

Can you help Rubel to find out the product of the even factors of 21?

Factors of 21 are 1, 3, 7, 21.
Even factors of 21 are 0.
Hence, product of even factors of 21 is; 0 = 0.