Factors of 21

The factors of 21 are 1, 3, 7 and 21

Negative Factors- These are negative counterparts of the positive factors.

Negative factors: -1, -3, -7, -21

 

Prime Factors - Prime factors are the prime numbers themselves, when multiplied together, give 21 as the product.
Prime factor: 3, 7 

 

Prime Factorization- Prime factorization involves breaking 21 into its prime factors

It is expressed as 3¹ × 7¹

 

Table listing the factors of 21

 

Positive Factors	1, 3, 7, 21
Negative Factors	-1, -3, -7, -21
Prime Factors	3,7
Prime Factorization	31 × 71

 

There are different methods to find the factors of 21.

 

Methods to find the factors of 21:

 

• Multiplication Method

 

• Division Method

 

• Prime Factor and Prime Factorization

 

• Factor Tree

The multiplication method finds the pair of factors that give 21 as their product.

 

Step-by-step process

 

Step 1: Find the pair of numbers whose product is 21. 

 

Step 2: The factors are those numbers, when multiplied, give 21.

 

Step 3: Make a list of numbers whose product will be 21.

 

A list of numbers whose products are 21 is given below:

 

1 × 21 = 21

3 × 7 = 21
 

The division method finds the numbers that fully divide the given number. 

Step-by-step process

 

Step 1: Since every number is divisible by 1, 1 will always be a factor.  Example: 21÷1 = 21

 

Step 2: Move to the next integer. Both divisor and quotient are the factors. 

 

Overview of Factors of 21 using the division method

 

Prime Factors of 21-There is only one prime factor for 21

Prime factors of 21: 3, 7

 

Steps to find the prime factors of 21

 

Step 1:  Divide 21 using the prime number 3

 

21÷3 = 7

 

Step 2: Divide 5 with the prime number 7

7÷7 = 1

Prime Factorization of 21- Prime Factorization breaks down the prime factors of 21

Expressed as 3¹ × 7¹
 

The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.

 

Factor Tree for 21:

 

 

Factors of 10 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

 
Positive Factor Pairs: (1,21), (3,7)

Negative Factor Pairs:  (-1,-21), (-3,-7)
 

• Divisor:  Number that divides another number

 

• Quotient: The number you get when you divide a number with another.

 

• Factors: Numbers that divide the given number, leaving zero as the remainder.

 

• Prime Factors: Prime numbers that multiply together to form the given number.

 

• Negative Factors: These are negative counterparts of the positive factors.