Divisors of 26

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: 26²

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 = 2¹ ×13¹

(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

=26²

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