All Divisors of 14

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.

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}

=14^4/2

=14²

=196

Related Topics:

• Divisors of numbers
• Factors of 14
• Divisors of 12
• Divisors of 15
• Divisors of 16

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