The divisors of 54 are those numbers that completely divide 54 with the remainder zero. In this section, we will discuss about divisors of 54.
Highlights of Divisors of 54
- Divisors of 54: 1, 2, 3, 6, 9, 18, 27 and 54
- Negative divisors of 54: -1, -2, -3, -6, -9, -18, -27 and -54
- Prime divisors of 54: 2 and 3
- Number of divisors of 54: 8
- Sum of divisors of 54: 120
- Product of divisors of 54: 544
What are Divisors of 54
A number n is a divisor of 54 if $\dfrac{54}{n}$ is an integer. Note that if 54/n=m is an integer, then both m and n will be the divisors of 54.
To find the divisors of 54, we need to find the numbers n such that 54/n becomes an integer. We have:
54/1=54 | 1, 54 are divisors of 54. |
54/2=27 | 2, 27 are divisors of 54 |
54/3=18 | 3, 18 are divisors of 54 |
54/6=9 | 6, 9 are divisors of 54 |
No numbers other than 1, 2, 3, 6, 9, 18, 27, and 54 can divide 54. So we conclude that
The divisors of 54 are: 1, 2, 3, 6, 9, 18, 27, and 54. |
Thus, the total number of divisors of 54 is eight.
Negative Divisors of 54
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54, we can say that:
The negative divisors of 54 are -1, -2, -3, -6, -9, -18, -27, and -54.
Prime Divisors of 54
The divisors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. Among these numbers, only 2 and 3 are prime numbers. So we obtain that:
The prime divisors of 54 are 2 and 3.
Video solution of Divisors of 54:
Sum, Product & Number of Divisors of 54
The prime factorization of 54 is given below.
54 = 21 × 33
(i) By the number of divisors formula, we have that the number of divisors of 54 is
=(1+1)(3+1)=2×4=8.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 54 is
$=\dfrac{2^2-1}{2-1} \times \dfrac{3^4-1}{3-1}$
$=\dfrac{4-1}{1} \times \dfrac{81-1}{2}$
$=3 \times 40=120$
(iii) By the product of divisors formula, we have that the product of the divisors of 54 is
=54(Number of divisors of 54)/2
=548/2
=544
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