# Find Divisors of 6

The divisors of 6 are those numbers that completely divide 6 with remainder zero. The divisors of 6 are 1, 2, 3, and 6. In this section, we will discuss about divisors of 6.

## Highlights of Divisors of 6

• Divisors of 6: 1, 2, 3 and 6
• Negative divisors of 6: -1, -2, -3 and -6
• Prime divisors of 6: 2 and 3
• Number of divisors of 6: 4
• Sum of divisors of 6: 12
• Product of divisors of 6: 62 =36.

## What are Divisors of 6

A number n is a divisor of 6 if $\dfrac{6}{n}$ is an integer. Thus, to find the divisors of 6, we need to find the numbers n such that 6/n becomes an integer. We have

No numbers other than 1, 2, 3, and 6 can divide 6. So the divisors of 6 are 1, 2, 3, and 6.

Thus, the total number of divisors of 6 is four.

## Negative Divisors of 6

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

As the divisors of 6 are 1, 2, 3, and 6, we can say that:

The negative divisors of 6 are -1, -2, -3, and –6.

## Prime Divisors of 6

The divisors of 6 are 1, 2, 3, and 6. Among these numbers, only 2 and 3 are prime numbers. So we obtain that:

The prime divisors of 6 are 2 and 3.

## Divisors of 6 Formula

The prime factorization of 6 is given below.

6 = 21 × 31

(i) By the number of divisors formula, we have that the number of divisors of 6 is

=(1+1)(1+1)=2×2=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 6 is

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

$=\dfrac{4-1}{1} \times \dfrac{9-1}{2}$

$=3 \times 4=12$

(iii) By the product of divisors formula, we have that the product of the divisors of 6 is

=6(Number of divisors of 6)/2

=64/2

=62

=36

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## Question Answer on Divisors of 6

Question 1: If A = x : x is a natural number that is a divisor of 6. Write A in roster form.

Solution:

We can write 6 as follows: 1×6=6, 2×3=6, 3×2=6. These are the only ways we can write 6 multiplicatively. Thus, the natural numbers 1, 2, 3, and 6 are divisors of 6. Hence, the roster form of A is

A = {1, 2, 3, 6}.

## FAQs on Divisors of 6

Q1: Find the divisors of 6.

Ans: The divisors of 6 are 1, 2, 3, and 6. So there are four divisors of 6.

Q2: Find the prime factorization of 6.

Ans: The prime factorization of 6 is 6=2×3.

Q3: Find the sum of the divisors of 6.

Ans: The sum of the divisors of 6 is 1+2+3+6 = 12.

Q4: What is the product of the divisors of 6.

Ans: The product of the divisors of 6 is 1×2×3×6 = 36.

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