The divisors of 28 are those numbers that completely divide 28 without a remainder. In this section, we will discuss about divisors of 28.
Table of Contents
Highlights of Divisors of 28
- Divisors of 28: 1, 2, 4, 7, 14 and 28
- Negative divisors of 28: -1, -2, -4, -7, -14 and -28
- Prime divisors of 28: 2 and 7
- Number of divisors of 28: 6
- Sum of divisors of 28: 56
- Product of divisors of 28: 283
What are Divisors of 28
A number n is a divisor of 28 if $\dfrac{28}{n}$ is an integer. Note that if 28/n=m is an integer, then both m and n will be the divisors of 28.
To find the divisors of 28, we need to find the numbers n such that 28/n becomes an integer. We have:
| 28/1=28 | 1, 28 are divisors of 28. |
| 28/2=14 | 2, 14 are divisors of 28 |
| 28/4=7 | 4, 7 are divisors of 28 |
No numbers other than 1, 2, 4, 7, 14, and 28 can divide 28. So we conclude that
|
The divisors of 28 are: 1, 2, 4, 7, 14, and 28. |
Thus, the total number of divisors of 28 is six.
Negative Divisors of 28
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 28 are 1, 2, 4, 7, 14, and 28, we can say that:
The negative divisors of 28 are -1, -2, -4, -7, -14, and –28.
Prime Divisors of 28
The divisors of 28 are 1, 2, 4, 7, 14, and 28. Among these numbers, only 2 and 7 are prime numbers. So we obtain that:
The prime divisors of 28 are 2 and 7.
Video solution of Divisors of 28:
Sum, Product & Number of Divisors of 28
The prime factorization of 28 is given below.
28 = 22 × 7
(i) By the number of divisors formula, we have that the number of divisors of 28 is
=(2+1)(1+1)=3×2=6.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 28 is
$=\dfrac{2^3-1}{2-1} \times \dfrac{7^2-1}{7-1}$
$=\dfrac{8-1}{1} \times \dfrac{49-1}{6}$
$=7 \times 8=56$
(iii) By the product of divisors formula, we have that the product of the divisors of 28 is
=28(Number of divisors of 28)/2
=286/2
=283
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