Definition of factors of 28: If a number completely divides 28 with the remainder zero, then that number is called a factor of 28. So we can say that the factors of 28 are the divisors of 28. In this section, we will learn about the factors of 28 and the prime factors of 28.
Table of Contents
Highlights of Factors of 28
- 28=2×2×7 is the prime factorization of 28.
- The factors of 28 are 1, 2, 4, 7, 14, and 28.
- Prime factors of 28 are 2 and 7.
- Negative factors of 28 are –1, -2, -4, -7, -14, and –28.
What are the factors of 28?
Let us write the number 28 multiplicatively in all possible ways. We have:
28 = 1×28
28 = 2×14
28 = 4×7
As we cannot express 28 multiplicatively in any other way, so we will stop right now. So the factors of 28 in pairs are given as follows:
| 28 = a×b | Factors in Pairs (a,b) |
| 28 = 1×28 | (1, 28) |
| 28 = 2×14 | (2, 14) |
| 28 = 4×7 | (4, 7) |
Thus the pair factors of 28 are (1, 28), (2, 14), and (4, 7). As all the numbers appearing in pair factors are the factors of 28, we conclude that
|
The factors of 28 are: 1, 2, 4, 7, 14, and 28. |
Number of factors of 28
From above we have calculated the factors of 28 which are 1, 2, 4, 7, 14, and 28. Thus the total number of factors of 28 is six.
Prime Factors of 28
Note that the factors of 28 are 1, 2, 4, 7, 14, and 28. Among those factors, we notice that only 2 and 7 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 28 are 2 and 7.
Also Read:
- Basic concepts of factors
- Square root of 28
Question: What are the factors of 28?
Video Solution of factors of 28:
How to find factors of 28?
Now we will determine the factors of 28 by division method. In this method, we will find the numbers that can divide 28 with no remainder.
| 28/1=28 and the remainder is 0. | ∴ 1 and 28 are factors of 28. |
| 28/2=14 and the remainder is 0. | ∴ 2 and 14 are factors of 28. |
| 28/4=7 and the remainder is 0. | ∴ 4 and 7 are factors of 28. |
Note that no numbers other than the numbers in violet color can divide 28. So the numbers in violet color, that is, 1, 2, 4, 7, 14, and 28 are the complete list of factors of 28.
