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 $\dfrac{56}{n}$ 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.
Video solution of Divisors of 56:
Sum, Product & Number of Divisors of 56
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
$=\dfrac{2^4-1}{2-1} \times \dfrac{7^2-1}{7-1}$
$=\dfrac{16-1}{1} \times \dfrac{49-1}{6}$
$=15 \times 8=120$
(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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