A number is said to be a divisor of 26 if that number completely divides 26 without a remainder. In this section, we will discuss about divisors of 26.

## Highlights of Divisors of 26

- Divisors of 26: 1, 2, 13 and 26
- Negative divisors of 26: -1, -2, -13 and -26
- Prime divisors of 26: 2 and 13
- Number of divisors of 26: 4
- Sum of divisors of 26: 42
- Product of divisors of 26: 26
^{2}

## What are Divisors of 26

A number n is a divisor of 26 if $\dfrac{26}{n}$ is an integer. Note that if 26/n=m is an integer, then both m and n will be the divisors of 26.

To find the divisors of 26, we need to find the numbers n such that 26/n becomes an integer. We have:

26/1=26 | 1, 26 are divisors of 26. |

26/2=13 | 2, 13 are divisors of 26 |

No numbers other than 1, 2, 13, and 26 can divide 26. So we conclude that

The divisors of 26 are: 1, 2, 13, and 26. |

Thus, the total number of divisors of 26 is four.

## Negative Divisors of 26

We know that if m is a divisor of a number, then -m is also a divisor of that number.

As the divisors of 26 are 1, 2, 13, and 26, we can say that:

The negative divisors of 26 are -1, -2, -13, and –26.

## Prime Divisors of 26

The divisors of 26 are 1, 2, 13, and 26. Among these numbers, only 2 and 13 are prime numbers. So we obtain that:

The prime divisors of 26 are 2 and 13.

Video solution of Divisors of 26:

## Sum, Product & Number of Divisors of 26

The prime factorization of 26 is given below.

26 = 2^{1 }×13^{1}

(i) By the number of divisors formula, we have that the number of divisors of 26 is

=(1+1)(1+1)=2×2=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 26 is

$=\dfrac{2^2-1}{2-1} \times \dfrac{13^2-1}{13-1}$

$=\dfrac{4-1}{1} \times \dfrac{169-1}{12}$

$=3 \times 14=42$

(iii) By the product of divisors formula, we have that the product of the divisors of 26 is

=26^{(Number of divisors of 26)/2}

=26^{4/2}

=26^{2}

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