Factors of 21
Factors of 21 are the numbers that divide 21 exactly without leaving any remainder. Understanding factors is an important part of mathematics because it helps students learn division, multiplication, prime factorization, and number relationships.
In this article, you will learn what the factors of 21 are, how to find them, factor pairs, prime factorization, and practical examples.
What Are the Factors of 21?
A factor of a number is any whole number that divides that number completely.
For 21, we check which numbers can divide 21 without leaving a remainder.
Division Method
- 21 ÷ 1 = 21
- 21 ÷ 3 = 7
- 21 ÷ 7 = 3
- 21 ÷ 21 = 1
Since these divisions leave no remainder, the factors of 21 are:
1, 3, 7, and 21
List of Factors of 21
The complete list of positive factors of 21 is:
1, 3, 7, 21
These are the only numbers that divide 21 exactly.
Factor Pairs of 21
Factor pairs are two numbers that multiply together to produce 21.
Positive Factor Pairs
- 1 × 21 = 21
- 3 × 7 = 21
Therefore, the factor pairs of 21 are:
- (1, 21)
- (3, 7)
Negative Factor Pairs
Since a negative number multiplied by another negative number gives a positive result, negative factor pairs also exist.
- (-1, -21)
- (-3, -7)
Prime Factorization of 21
Prime factorization means expressing a number as a product of prime numbers.
Let’s factor 21:
21 ÷ 3 = 7
Both 3 and 7 are prime numbers.
Therefore:
21 = 3 × 7
Prime factorization of 21:
3 × 7
Or written using exponents:
3¹ × 7¹
Is 21 a Prime Number?
No, 21 is not a prime number.
A prime number has exactly two factors: 1 and itself.
Since 21 has four factors (1, 3, 7, and 21), it is a composite number.
Is 21 an Odd Number?
Yes, 21 is an odd number because it is not divisible by 2.
All odd numbers end in 1, 3, 5, 7, or 9, and 21 ends in 1.
How to Find Factors of 21
Follow these simple steps:
Step 1
Start with the number 1.
1 divides every number, so 1 is a factor.
Step 2
Check each whole number up to the square root of 21.
- 2 does not divide 21 exactly.
- 3 divides 21 exactly.
Step 3
Find the corresponding factor.
Since 21 ÷ 3 = 7, both 3 and 7 are factors.
Step 4
Include the number itself.
21 is always a factor of 21.
Final factors:
1, 3, 7, 21
Solved Examples
Example 1
How many factors does 21 have?
Factors of 21:
1, 3, 7, 21
Answer: 4 factors
Example 2
What is the greatest factor of 21?
The largest factor of any number is the number itself.
Answer: 21
Example 3
What is the sum of all factors of 21?
Factors:
1 + 3 + 7 + 21 = 32
Answer: 32
Example 4
Which factors of 21 are prime?
Factors of 21:
1, 3, 7, 21
Prime factors:
3 and 7
Applications of Factors
Factors are useful in:
- Solving mathematical problems
- Simplifying fractions
- Finding common factors
- Learning prime factorization
- Understanding divisibility rules
- Algebra and number theory
Key Points to Remember
- Factors of 21 are 1, 3, 7, and 21.
- 21 has four positive factors.
- Factor pairs are (1, 21) and (3, 7).
- Prime factorization of 21 is 3 × 7.
- 21 is a composite number.
- 21 is an odd number.
FAQs About Factors of 21
What are the factors of 21?
The factors of 21 are:
1, 3, 7, and 21
How many factors does 21 have?
21 has 4 positive factors.
What are the factor pairs of 21?
The factor pairs of 21 are:
- (1, 21)
- (3, 7)
What is the prime factorization of 21?
The prime factorization of 21 is:
3 × 7
Is 21 a prime number?
No, 21 is a composite number because it has more than two factors.
Is 7 a factor of 21?
Yes, because:
21 ÷ 7 = 3
Therefore, 7 is a factor of 21.
What is the greatest factor of 21?
The greatest factor of 21 is 21.
What is the smallest factor of 21?
The smallest positive factor of 21 is 1.
Are 3 and 7 factors of 21?
Yes. Both divide 21 exactly without leaving a remainder.
What is the sum of all factors of 21?
1 + 3 + 7 + 21 = 32
So, the sum of all factors of 21 is 32.
Conclusion
The factors of 21 are 1, 3, 7, and 21. These numbers divide 21 exactly with no remainder. Understanding factors helps students build a strong foundation in mathematics, especially in multiplication, division, prime factorization, and number theory. Since 21 can be expressed as 3 × 7, it is a composite number with four positive factors.
