Definition of factors of 22: If a number completely divides 22 with the remainder zero, then that number is called a factor of 22. So the factors of 22 are the divisors of 22. In this section, we will learn about the factors of 22 and the prime factors of 22.
Table of Contents
Highlights of Factors of 22
- 22=2×11 is the prime factorization of 22.
- The factors of 22 are 1, 2, 11, and 22.
- Prime factors of 22 are 2 and 11.
- Negative factors of 22 are -1, -2, -11 and -22.
What are the Factors of 22?
At first, we will find the factors of 22 by the multiplication method. Let us write the number 22 multiplicatively in all possible ways. We have:
| 22 = 1×22 | ∴ 1, 22 are factors of 22 |
| 22 = 2×11 | ∴ 2, 11 are factors of 22 |
We see that it is not possible to express 22 multiplicatively in any other way, so we will stop right now. Thus all the factors of 22 are 1, 2, 11, and 22.
If m is a factor of 22, then -m is also a factor of 22. So all the negative factors of 22 are -1, -2, -11, and -22.
Pair Factors of 22
| 22 = a×b | Pair Factors of 22 |
| 22 = 1×22 | (1, 22) |
| 22 = 2×11 | (2, 11) |
Thus the positive pair factors of 22 are (1, 22) and (2, 11). We know that if (a, b) is a positive pair factor of 22, then (-a, -b) is a negative pair factor of 22. Using this fact we get all the negative pair factors of 22, and they are (-1, -22) and (-2, -11).
Number of Factors of 22
From above we have calculated the factors of 22 which are 1, 2, 11, and 22. Thus the total number of factors of 22 is four.
Prime Factors of 22
Note that the factors of 22 are 1, 2, 11, and 22. Among those factors, we observe that only 2 and 11 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 22 are 2 and 11.
Also Read:
| Factors of 33: | 1, 3, 11, 33 |
| Factors of 12: | 1, 2, 3, 4, 6, 12 |
| Factors of 42: | 1, 2, 3, 6, 7, 14, 21, 42 |
| Factors of 51: | 1, 3, 17, 51 |
Question: What are the factors of 22?
Video Solution: coming soon…
How to Find Factors of 22?
Now we will determine the factors of 22 by division method. In this method, we will find the numbers that can divide 22 with no remainder. See that
| 22/1=22 and the remainder is 0. | ∴ 1 and 22 are factors of 22. |
| 22/2=11 and the remainder is 0. | ∴ 2 and 11 are factors of 22. |
Note that no numbers other than the numbers in violet color can divide 22. So the numbers in violet color, that is, 1, 2, 11, and 22 are the complete list of factors of 22.
