# Divisors of 56

The divisors of 56 are those numbers that completely divide 56 with the remainder zero. In this section, we will discuss about divisors of 56.

#### Highlights of Divisors of 56

• Divisors of 56: 1, 2, 4, 7, 8, 14, 28 and 56
• Negative divisors of 56: -1, -2, -4, -7, -8, -14, -28 and -56
• Prime divisors of 56: 2 and 7
• Number of divisors of 56: 8
• Sum of divisors of 56: 120
• Product of divisors of 56: 564

#### What are Divisors of 56

A number n is a divisor of 56 if $\frac{56}{n}$ is an integer. Note that if 56/n=m is an integer, then both m and n will be the divisors of 56.

To find the divisors of 56, we need to find the numbers n such that 56/n becomes an integer. We have:

 56/1=56 1, 56 are divisors of 56. 56/2=28 2, 28 are divisors of 56 56/4=14 4, 14 are divisors of 56 56/7=8 7, 8 are divisors of 56

No numbers other than 1, 2, 4, 7, 8, 14, 28 and 56 can divide 56. So we conclude that

 The divisors of 56 are: 1, 2, 4, 7, 8, 14, 28 and 56.

Thus, the total number of divisors of 56 is eight.

#### Negative Divisors of 56

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

As the divisors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56, we can say that:

The negative divisors of 56 are -1, -2, -4, -7, -8, -14, -28 and -56.

#### Prime Divisors of 56

The divisors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56. Among these numbers, only 2 and 7 are prime numbers. So we obtain that:

The prime divisors of 56 are 2 and 7.

Key Things

The prime factorization of 56 is given below.

56 = 23 × 71

(i) By the number of divisors formula, we have that the number of divisors of 56 is

=(3+1)(1+1)=4×2=8.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 56 is

$=\frac{2^4-1}{2-1} \times \frac{7^2-1}{7-1}$

$=\frac{16-1}{1} \times \frac{49-1}{6}$

$=15 \times 8=120$

(iii) By the product of divisors formula, we have that the product of the divisors of 56 is

=56(Number of divisors of 56)/2

=568/2

=564

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