# Divisors of 44

The divisors of 44 are those numbers that completely divide 44 without a remainder. In this section, we will discuss about divisors of 44.

#### Highlights of Divisors of 44

• Divisors of 44: 1, 2, 4, 11, 22 and 44
• Negative divisors of 44: -1, -2, -4, -11, -22 and -44
• Prime divisors of 44: 2 and 11
• Number of divisors of 44: 6
• Sum of divisors of 44: 84
• Product of divisors of 44: 443

#### What are Divisors of 44

A number n is a divisor of 44 if $\frac{44}{n}$ is an integer. Note that if 44/n=m is an integer, then both m and n will be the divisors of 44.

To find the divisors of 44, we need to find the numbers n such that 44/n becomes an integer. We have:

 44/1=44 1, 44 are divisors of 44. 44/2=22 2, 22 are divisors of 44 44/4=11 4, 11 are divisors of 44

No numbers other than 1, 2, 4, 11, 22 and 44 can divide 44. So we conclude that

 The divisors of 44 are: 1, 2, 4, 11, 22 and 44.

Thus, the total number of divisors of 44 is six.

#### Negative Divisors of 44

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

As the divisors of 44 are 1, 2, 4, 11, 22, and 44, we can say that:

The negative divisors of 44 are -1, -2, -4, -11, -22, and –44.

#### Prime Divisors of 44

The divisors of 44 are 1, 2, 4, 11, 22, and 44. Among these numbers, only 2 and 11 are prime numbers. So we obtain that:

The prime divisors of 44 are 2 and 11.

Key Things

The prime factorization of 44 is given below.

44 = 22 × 111

(i) By the number of divisors formula, we have that the number of divisors of 44 is

=(2+1)(1+1)=3×2=6.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 44 is

$=\frac{2^3-1}{2-1} \times \frac{11^2-1}{11-1}$

$=\frac{8-1}{1} \times \frac{121-1}{10}$

$=7 \times 12=84$

(iii) By the product of divisors formula, we have that the product of the divisors of 44 is

=44(Number of divisors of 44)/2

=446/2

=443

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