Divisors of 4

The divisors of 4 are those numbers that completely divide 4 without a remainder. In this section, we will discuss about divisors of 4.

Highlights of Divisors of 4

  • Divisors of 4: 1, 2 and 4
  • Negative divisors of 4: -1, -2 and -4
  • Prime divisors of 4: 2
  • Number of divisors of 4: 3
  • Sum of divisors of 4: 7
  • Product of divisors of 4: 43/2 =23=8.

 

What are Divisors of 4

A number n is a divisor of 4 if $\frac{4}{n}$ is an integer. Note that if 4/n=m is an integer, then both m and n will be the divisors of 4.

To find the divisors of 4, we need to find the numbers n such that 4/n becomes an integer. We have:

4/1=4 1, 4 are divisors of 4.
4/2=2 2 is a divisor of 4

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

The divisors of 4 are:

1, 2 and 4.

Thus, the total number of divisors of 4 is three.

 

Negative Divisors of 4

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

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

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

 

Prime Divisors of 4

The divisors of 4 are 1, 2, and 4. Among these numbers, only 2 is a prime number. So we obtain that:

The only prime divisor of 4 is 2.

 

Key Things

The prime factorization of 4 is given below.

4 = 22

(i) By the number of divisors formula, we have that the number of divisors of 4 is

=(2+1)=3.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 4 is

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

$=\frac{8-1}{1}$

$=7$

(iii) By the product of divisors formula, we have that the product of the divisors of 4 is

=4(Number of divisors of 4)/2

=43/2

=23

=8

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