Factors of 21

Factors of 21 are integers that can be divided evenly into 21. It has a total of 4 factors of which 21 is the biggest factor and the positive factors of 21 are 1, 3, 7, and 21. The sum of all factors of 21 is 32 and its factors in Pairs are (1, 21) and (3, 7).

• Factors of 21: 1, 3, 7 and 21
• Negative Factors of 21: -1, -3, -7 and -21
• Prime Factors of 21: 3, 7
• Prime Factorization of 21: 3 × 7 = 3 × 7
• Sum of Factors of 21: 32

What are the Factors of 21?

To have an answer to this question let us have a look at the following facts about factors of 21:

• The factor of 21 is that number that divides 21 completely i.e., without any remainder.
• The number 21 is composite. To understand why it is composite, let's recall the definition of a composite number. "A number is said to be composite if it has more than two factors
• The factors of 21 are all the integers that divide 21 without any remainder.
• According to the definition, the justified factors of 21 are 1, 3, 7, and 21.

How to Calculate the Factors of 21?

Let's begin calculating the factors of 21, starting with the smallest whole number i.e. 1

• Divide 21 with this number. Is the remainder 0?
• 21 ÷ 1 = 21
• The next whole number is 3
• 21 ÷ 3 = 7 
• The next whole number is 7
• 21 ÷ 7 = 3

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

Explore factors using illustrations and interactive examples.

• Factors of 121 - The factors of 121 are 1, 11, 121
• Factors of 210 - The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
• Factors of 216 - The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
• Factors of 27 - The factors of 27 are 1, 3, 9, 27
• Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
• Factors of 35 - The factors of 35 are 1, 5, 7, 35

Factors of 21 by Prime Factorization

"Prime factorization means to express a composite number as the product of its prime factors." To get the prime factorization of 21, we will follow the below process:

• Divide 21 by its prime factor, say 3
• 21 ÷ 3 = 7
• 7 is divided by its prime factor and the quotient is obtained.
• This process goes on till we get the quotient as 1
• 7 ÷ 7 = 1  
• We find that 21 has a total of 2 prime factors.

The prime factorization of 21 is shown below:

Factors of 21 in Pairs

The pair of numbers which gives 32 when multiplied is known as factor pairs of 21. The following are the factors of 21 in pairs.

• Observe in the table above, after 3 × 7, the factors start repeating accept the order.
• So, it is enough to find factors until (3, 7)
• Pairs of factors of 21 are: (1, 21), (3, 7)

Fractions or decimals cannot be the factors. Only integers (positive or negative) can be the factors.

• Factors of 21 are 1, 3, 7, and 21.