The divisors of 14 are 1, 2, 7, and 14. The divisors of 14 are those numbers that completely divide 14 without leaving a remainder. In this section, we will discuss divisors of 14.
Table of Contents
Highlights of Divisors of 14
- Divisors of 14: 1, 2, 7 and 14
- Negative divisors of 14: -1, -2, -7 and -14
- Prime divisors of 14: 2 and 7
- Number of divisors of 14: 4
- Sum of divisors of 14: 24
- Product of divisors of 14: 142 =196.
What are Divisors of 14
A number n is said to be a divisor of 14 if the fraction $\dfrac{14}{n}$ becomes an integer. Note that if 14/n=m is an integer, then both m and n will be the divisors of 14.
To find the divisors of 14, we need to find the numbers n such that 14/n becomes an integer. We have:
| 14/1=14 | 1, 14 are divisors of 14. |
| 14/2=7 | 2, 7 are divisors of 14 |
No numbers other than 1, 2, 7, and 14 can divide 14. So we conclude the following.
| The divisors of 14 are 1, 2, 7, and 14. |
So the total number of divisors of 14 is four.
Negative Divisors of 14
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 14 are 1, 2, 7, and 14, we can say that:
The negative divisors of 14 are -1, -2, -7, and –14.
Prime Divisors of 14
The divisors of 14 are 1, 2, 7, and 14. Among these numbers, only 2 and 7 are prime numbers. So we obtain that:
The prime divisors of 14 are 2 and 7.
Video solution of Divisors of 14:
Sum, Product & Number of Divisors of 14
The prime factorization of 14 is given below.
14 = 21 × 71
(i) By the number of divisors formula, we have that the number of divisors of 14 is
=(1+1)(1+1)=2×2=4.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 14 is
$=\dfrac{2^2-1}{2-1} \times \dfrac{7^2-1}{7-1}$
$=\dfrac{4-1}{1} \times \dfrac{49-1}{6}$
$=3 \times 8=24$
(iii) By the product of divisors formula, we have that the product of the divisors of 14 is
=14(Number of divisors of 14)/2
=144/2
=142
=196
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FAQs
Answer: The divisors of 14 are 1, 2, 7, and 14.
Answer: Yes, 7 is a divisor of 14 as 7 divides 14 completely.
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