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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