# 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.

## 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

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

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

$=7 \times 6=42$

(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

=206/2

=203

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## FAQs on Divisors of 20

Q1: What are the divisors of 20?

Answer: The divisors of 20 are 1, 2, 4, 5, 10, and 20. So there are six divisors of 20.

Q2: Find the product of divisors of 20?

Answer: The product of divisors of 20 is = 1 × 2 × 4 × 5 × 10 × 20 = 8000.