# Divisors of 28

The divisors of 28 are those numbers that completely divide 28 without a remainder. In this section, we will discuss about divisors of 28.

#### 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 $\frac{28}{n}$ 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.

Key Things

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

$=\frac{2^3-1}{2-1} \times \frac{7^2-1}{7-1}$

$=\frac{8-1}{1} \times \frac{49-1}{6}$

$=7 \times 8=56$

(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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