Divisors of 14

The divisors of 14 are those numbers that completely divide 14 without a remainder. In this section, we will discuss about divisors of 14.

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 a divisor of 14 if $\frac{14}{n}$ is 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 that

The divisors of 14 are:

1, 2, 7 and 14.

Thus, 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.

 

Key Things

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

$=\frac{2^2-1}{2-1} \times \frac{7^2-1}{7-1}$

$=\frac{4-1}{1} \times \frac{49-1}{6}$

$=3 \times 8=24$

(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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