How to Find All Factors of 21 Using Division Method
The concept of factors of 21 is fundamental in mathematics. Whether for school exams, homework, or understanding divisibility, learning how to find the factors of 21 makes calculation and number manipulation much easier. This topic is also useful for topics like HCF, LCM, and prime factorization.
What Are Factors of 21?
A factor of 21 is a number that divides 21 exactly with no remainder. In simple words, the factors of 21 are all whole numbers that can be multiplied by another whole number to result in 21. You’ll find this concept applied in prime factorization, factor trees, and divisibility tests.
List of Positive and Negative Factors of 21
The factors of 21 include both positive and negative numbers, since a positive times a negative (or negative times a positive) also gives 21. Let’s look at all factors:
| Positive Factors | Negative Factors |
|---|---|
| 1, 3, 7, 21 | -1, -3, -7, -21 |
Factor Pairs of 21
Factor pairs are two numbers that multiply to give 21. Here are all the possible pairs:
| Pair 1 | Pair 2 | Product |
|---|---|---|
| 1 | 21 | 1 × 21 = 21 |
| 3 | 7 | 3 × 7 = 21 |
| -1 | -21 | -1 × -21 = 21 |
| -3 | -7 | -3 × -7 = 21 |
Prime Factorization of 21
Prime factorization is the process of expressing 21 as a product of its prime factors. This method is widely used for finding HCF and LCM. Here’s how to break down the number:
1. Start with 21. What is the smallest prime number that divides 21? It’s 3.2. Divide 21 by 3: 21 ÷ 3 = 7.
3. Next, check 7. 7 is a prime number.
4. So, the prime factorization is: 21 = 3 × 7
This method is called factor tree. Both 3 and 7 are prime factors. The prime factors of 21 are 3 and 7.
Is 21 a Prime or Composite Number?
A prime number has only two factors: 1 and itself. But 21 has four positive factors (1, 3, 7, and 21). That means 21 is a composite number. It can be divided by numbers other than 1 and 21. So, when asked "Is 21 a prime number?" — the answer is NO, it is composite.
How to Find Factors of 21 (Stepwise Method)
Follow these steps to find factors of 21:
1. Start with 1. 21 ÷ 1 = 21 (so 1 and 21 are factors).2. Try 2. 21 ÷ 2 = 10.5 (not a whole number, so skip).
3. Try 3. 21 ÷ 3 = 7 (so 3 and 7 are factors).
4. Try 4, 5, 6. None give a whole number result.
5. Stop at 7 (since factors start repeating in reverse).
So, the factors of 21 are 1, 3, 7, 21.
Speed Trick: Spotting Factors Fast!
Quick Trick: If the sum of the digits is a multiple of 3, then 21 is divisible by 3 (since 2 + 1 = 3). This trick helps you find factors of 21 quickly during exams!
Relation to Other Maths Concepts
The idea of factors of 21 is useful in finding HCF (LCM and HCF), simplifying fractions, as well as solving word problems involving grouping or divisibility. Learning factorization also builds the base for studying prime factorization and multiples.
Practice Problems: Try These Yourself!
- List all factors of 21 in pairs.
- Is 21 an even number?
- Is 21 a perfect square?
- Find common factors between 21 and 35.
- What are the prime factors of 21?
Common Mistakes and Tips
- Missing factor pairs by stopping checks too early (stop at √21, not 21).
- Confusing multiples with factors. Remember: factors divide into 21, multiples come from multiplying 21.
- Forgetting negative factors — for exams that ask for all integer factors, include negatives!
Classroom Tip
To quickly spot factors of 21, remember: 1 and 21 are always included, and check all numbers up to √21. Pair those that "fit" as factor pairs. At Vedantu, teachers encourage students to draw quick factor trees for better memory and visualization.
We explored factors of 21—from definition, list, prime factorization, pairs, calculation steps, and quick-check tricks. Keep practicing with Vedantu’s tips and live examples to become a pro at finding factors for any number!
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FAQs on What Are the Factors of 21 in Maths
1. What are the factors of 21?
The factors of 21 are 1, 3, 7, and 21. These are the positive integers that divide 21 exactly without leaving a remainder.
- 21 ÷ 1 = 21
- 21 ÷ 3 = 7
- 21 ÷ 7 = 3
- 21 ÷ 21 = 1
2. How do you find the factors of 21?
You can find the factors of 21 by checking which numbers divide 21 exactly without a remainder.
- Start from 1 and go up to 21.
- Test division: 21 ÷ 1, 21 ÷ 2, 21 ÷ 3, and so on.
- Select numbers that give whole number answers.
3. Is 21 a prime or composite number?
The number 21 is a composite number because it has more than two factors. A prime number has exactly two factors (1 and itself), but 21 has four factors: 1, 3, 7, and 21. Therefore, 21 is not prime.
4. What is the prime factorization of 21?
The prime factorization of 21 is 3 × 7. Both 3 and 7 are prime numbers, and multiplying them gives 21.
- 21 ÷ 3 = 7
- 7 is a prime number
5. What are the factor pairs of 21?
The factor pairs of 21 are (1, 21) and (3, 7). Factor pairs are two numbers that multiply together to give 21.
- 1 × 21 = 21
- 3 × 7 = 21
6. What are the common factors of 21 and 14?
The common factors of 21 and 14 are 1 and 7.
- Factors of 21: 1, 3, 7, 21
- Factors of 14: 1, 2, 7, 14
7. What is the greatest common factor (GCF) of 21 and 28?
The greatest common factor (GCF) of 21 and 28 is 7.
- Factors of 21: 1, 3, 7, 21
- Factors of 28: 1, 2, 4, 7, 14, 28
8. What are the multiples of 21?
The multiples of 21 are numbers obtained by multiplying 21 by whole numbers.
- 21 × 1 = 21
- 21 × 2 = 42
- 21 × 3 = 63
- 21 × 4 = 84
9. How many factors does 21 have?
The number 21 has 4 factors. These factors are 1, 3, 7, and 21. Since there are four positive integers that divide 21 exactly, the total number of factors is 4.
10. Why is 7 a factor of 21?
The number 7 is a factor of 21 because it divides 21 exactly with no remainder.
- 21 ÷ 7 = 3
