How to Find the Factors of 21 Using Division and Prime Factorization
Before we start explaining what are the factors of 21, we have first to understand what factors are. When we multiply two numbers, we get a product, and these products put quite simply are factors of a number. An example of this can be when we divide the number 3 by 6; we get 5. So, in other words, it can be said that both numbers 6 and 5 are the factors of the number 3. There are various ways by which we can find the factors of a particular number which we would need to discuss before knowing what are the factors of 21.
Prime Factorization Method
We would have to understand the prime factorization method before finding the factors of 21. Prime factorization is quite simply put is finding the different prime numbers that multiply to provide a given number. The best way to go about this method is to divide the number by the smallest prime number (that is the number 2) and continue the method with higher prime numbers. This method can be applied to find the factors of 21, although the answers would be in the form of the product of prime numbers only which can be changed to different products as per requirement. Prime factorisation of 21 gives the result quickly.
Pair Factors of 21
Now what are the factors of 21? 21 is not a prime number and hence would be divisible by other prime numbers. To find the pair factors of 21, we would need to find both the positive as well as the negative factors of 21. The multiplications of these two numbers would give the product 21. These numbers are 1 and 21, which give the product 21. 7 and 3 when multiplied also give 21. Thus, (1,21) and (3,7) are both pair factors of the number 21. This gives all factors of 21.
Steps to Calculate Factors of 21
Before calculating all factors of 21, one needs to first learn the method and steps to calculate the factors of 21. The first step in this process is obviously to write the number 21 and to try to find out the two numbers that would give the result as 21. These can be 7 and 3 or 21 and 1. We already know that 3 is a prime number. 2 and 5 are examples of a prime number.
In the case of 21, we can see that the least prime number 21 is divisible by 3. When we divide the number 21 by 3, we get the quotient as 7. Thus, 7 and 3 must both be factors of 21. 7 is a prime number as well since it is divisible by no other number than 7 and 1. In the final step, we have to write the different unique numbers which would be obtained as factors of the number 21.
Division Method to Obtain Prime Factors of 21
We know that 21 is a composite number; in other words, it is not only divisible by 21 and 1 but by other numbers as well. Hence, the number 21 must-have different prime factors. The steps to calculate the prime factors of 21 is relatively easy. The first step in this method is to divide the number 21 by a prime factor. The smallest prime factor that can divide the 21 is 3. When we divide 21 by 3, we get the quotient as 7. Hence 7 and 3 multiplied must give the product 21. If we are to divide the number 7 by 3, we will provide results in decimal, so we move on to the next prime number. However, we will see that we cannot proceed any further than 7 and hence 3 and 7 are the only two prime factors of the number 21.
Did You Know?
Factors are a term which is a part of multiplication in mathematics. The divisor is an integer that would divide a number and not leave any remainder behind—in the process of integer factorization, breaking down the object into various numbers whose product would give us the given number. One may also ask how the concept of prime numbers came into being. While it is difficult to put an estimate about the date of the invention of prime numbers, it has been seen that the concept of prime numbers dates back to ancient Greece. So, it is pretty evident that the concept of factors and prime numbers has been known for quite a while in human history.
Solved Example:
Q. Find the factors of 21.
Answer: All the factors of 21 are 7, 3, 1 and 21. If we divide 21 by 3, we get the number 7. Thus 7 and 3 multiplied must give the number 21.
FAQs on Factors of 21 Explained with Simple Methods
1. What are the factors of 21?
The factors of 21 are 1, 3, 7, and 21. These are the numbers 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?
To find the factors of 21, divide 21 by natural numbers and check which ones leave no remainder.
- Step 1: Start with 1 and divide 21 by 1.
- Step 2: Continue checking 2, 3, 4, and so on.
- Step 3: Stop once you reach the square root of 21 (about 4.5).
3. What is the prime factorization of 21?
The prime factorization of 21 is 3 × 7. Both 3 and 7 are prime numbers.
- 21 ÷ 3 = 7
- 7 is a prime number
4. Is 21 a prime or composite number?
The number 21 is a composite number because it has more than two factors.
- Factors of 21: 1, 3, 7, 21
- A prime number has exactly two factors: 1 and itself
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. How many factors does 21 have?
The number 21 has 4 positive factors. These are 1, 3, 7, and 21.
- 1 and 21
- 3 and 7
7. What is the sum of all factors of 21?
The sum of the factors of 21 is 32. Add all its positive factors together:
- 1 + 3 + 7 + 21 = 32
8. What is the difference between factors and multiples of 21?
The factors of 21 divide 21 exactly, while multiples of 21 are numbers obtained by multiplying 21 by integers.
- Factors: 1, 3, 7, 21
- Multiples: 21, 42, 63, 84, …
9. Are 3 and 7 factors of 21?
Yes, 3 and 7 are factors of 21 because they divide 21 exactly without leaving a remainder.
- 21 ÷ 3 = 7
- 21 ÷ 7 = 3
10. Can you find the factors of 21 using a factor tree?
Yes, you can use a factor tree to find the prime factors of 21, which are 3 and 7.
- Start with 21
- Split 21 into 3 × 7
- Since 3 and 7 are prime, stop there
