Divisors of 20

The divisors of 20 are those numbers that completely divide 20 with the remainder zero. In this section, we will discuss about divisors of 20.

Highlights of Divisors of 20

• Divisors of 20: 1, 2, 4, 5, 10 and 20
• Negative divisors of 20: -1, -2, -4, -5, -10 and -20
• Prime divisors of 20: 2 and 5
• Number of divisors of 20: 6
• Sum of divisors of 20: 42
• Product of divisors of 20: 20³

What are Divisors of 20

A number n is a divisor of 20 if $\frac{20}{n}$ is an integer. Note that if 20/n=m is an integer, then both m and n will be the divisors of 20.

To find the divisors of 20, we need to find the numbers n such that 20/n becomes an integer. We have:

20/1=20	1, 20 are divisors of 20.
20/2=10	2, 10 are divisors of 20
20/4=5	4, 5 are divisors of 20

No numbers other than 1, 2, 4, 5, 10, and 20 can divide 20. So we conclude that

The divisors of 20 are: 1, 2, 4, 5, 10, and 20.

Thus, the total number of divisors of 20 is six.

Negative Divisors of 20

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

As the divisors of 20 are 1, 2, 4, 5, 10, and 20, we can say that:

The negative divisors of 20 are -1, -2, -4, -5, -10, and –20.

Prime Divisors of 20

The divisors of 20 are 1, 2, 4, 5, 10, and 20. Among these numbers, only 2 and 5 are prime numbers. So we obtain that:

The prime divisors of 20 are 2 and 5.

Video solution of Divisors of 20:

Formulas related to Divisors of 20

The prime factorization of 20 is given below.

20 = 2²×5¹

(i) By the number of divisors formula, we have that the number of divisors of 20 is

=(2+1)(1+1)=3×2=6.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 20 is

$=\dfrac{2^3-1}{2-1} \times \dfrac{5^2-1}{5-1}$

$=\dfrac{8-1}{1} \times \dfrac{25-1}{4}$

$=7 \times 6=42$

(iii) By the product of divisors formula, we have that the product of the divisors of 20 is

=20^{(Number of divisors of 20)/2}

=20^6/2

=20³

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