The factors of 21 are the numbers that completely divide 21 with the remainder zero. So we can say that the factors of 21 are the divisors of 21. In this section, we will learn about the factors of 21 and the prime factors of 21.
Table of Contents
Highlights of Factors of 21
- 21=3×7 is the prime factorization of 21.
- The factors of 21 are 1, 3, 7, and 21.
- Prime factors of 21 are 3 and 7.
- Negative factors of 21 are –1, -3, -7, and –21.
What are the Factors of 21?
Let us write the number 21 multiplicatively in all possible ways. We have:
21 = 1×21
21 = 3×7
As we cannot express 21 multiplicatively in any other way, so we will stop right now. So the factors of 21 in pairs are given as follows:
| 21 = a×b | Factors in Pairs (a,b) |
| 21 = 1×21 | (1, 21) |
| 21 = 3×7 | (3, 7) |
Thus the pair factors of 21 are (1, 21) and (3, 7). As all the numbers appearing in pair factors are the factors of 21, we conclude that
|
The factors of 21 are: 1, 3, 7, and 21. |
Number of Factors of 21
From above we have calculated the factors of 21 which are 1, 3, 7, and 21. Thus the total number of factors of 21 is four.
Prime Factors of 21
Note that the factors of 21 are 1, 3, 7, and 21. Among those factors, we notice that only 3 and 7 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 21 are 3 and 7.
Also Read: Basic concepts of factors
Question: What are the factors of 21?
Video Solution: coming soon…
How to Find Factors of 21?
Now we will determine the factors of 21 by division method. In this method, we will find the numbers that can divide 21 with no remainder.
| 21/1=21 and the remainder is 0. | ∴ 1 and 21 are factors of 21. |
| 21/3=7 and the remainder is 0. | ∴ 3 and 7 are factors of 21. |
Note that no numbers other than the numbers in violet color can divide 21. So the numbers in violet color, that is, 1, 3, 7, and 21 are the complete list of factors of 21.
