The divisors of 20 are those numbers that completely divide 20 with the remainder zero. In this section, we will discuss about divisors of 20.
Highlights of Divisors of 20
- Divisors of 20: 1, 2, 4, 5, 10 and 20
- Negative divisors of 20: -1, -2, -4, -5, -10 and -20
- Prime divisors of 20: 2 and 5
- Number of divisors of 20: 6
- Sum of divisors of 20: 42
- Product of divisors of 20: 203
What are Divisors of 20
A number n is a divisor of 20 if $\frac{20}{n}$ is an integer. Note that if 20/n=m is an integer, then both m and n will be the divisors of 20.
To find the divisors of 20, we need to find the numbers n such that 20/n becomes an integer. We have:
20/1=20 | 1, 20 are divisors of 20. |
20/2=10 | 2, 10 are divisors of 20 |
20/4=5 | 4, 5 are divisors of 20 |
No numbers other than 1, 2, 4, 5, 10, and 20 can divide 20. So we conclude that
The divisors of 20 are: 1, 2, 4, 5, 10, and 20. |
Thus, the total number of divisors of 20 is six.
Negative Divisors of 20
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 20 are 1, 2, 4, 5, 10, and 20, we can say that:
The negative divisors of 20 are -1, -2, -4, -5, -10, and –20.
Prime Divisors of 20
The divisors of 20 are 1, 2, 4, 5, 10, and 20. Among these numbers, only 2 and 5 are prime numbers. So we obtain that:
The prime divisors of 20 are 2 and 5.
Video solution of Divisors of 20:
Formulas related to Divisors of 20
The prime factorization of 20 is given below.
20 = 22×51
(i) By the number of divisors formula, we have that the number of divisors of 20 is
=(2+1)(1+1)=3×2=6.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 20 is
$=\dfrac{2^3-1}{2-1} \times \dfrac{5^2-1}{5-1}$
$=\dfrac{8-1}{1} \times \dfrac{25-1}{4}$
$=7 \times 6=42$
(iii) By the product of divisors formula, we have that the product of the divisors of 20 is
=20(Number of divisors of 20)/2
=206/2
=203
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FAQs on Divisors of 20
Answer: The divisors of 20 are 1, 2, 4, 5, 10, and 20. So there are six divisors of 20.
Answer: The product of divisors of 20 is = 1 × 2 × 4 × 5 × 10 × 20 = 8000.