A number is said to be a divisor of 34 if that number completely divides 34 with the remainder zero. In this section, we will discuss about divisors of 34.
Table of Contents
Highlights of Divisors of 34
- Divisors of 34: 1, 2, 17 and 34
- Negative divisors of 34: -1, -2, -17 and -34
- Prime divisors of 34: 2 and 17
- Number of divisors of 34: 4
- Sum of divisors of 34: 54
- Product of divisors of 34: 342
What are Divisors of 34
A number n is a divisor of 34 if $\dfrac{34}{n}$ is an integer. Note that if 34/n=m is an integer, then both m and n will be the divisors of 34.
To find the divisors of 34, we need to find the numbers n such that 34/n becomes an integer. We have:
| 34/1=34 | 1, 34 are divisors of 34. |
| 34/2=17 | 2, 17 are divisors of 34 |
No numbers other than 1, 2, 17, and 34 can divide 34. So we conclude that
|
The divisors of 34 are: 1, 2, 17, and 34. |
Thus, the total number of divisors of 34 is four.
Negative Divisors of 34
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 34 are 1, 2, 17, and 34, we can say that:
The negative divisors of 34 are -1, -2, -17, and –34.
Prime Divisors of 34
The divisors of 34 are 1, 2, 17, and 34. Among these numbers, only 2 and 17 are prime numbers. So we obtain that:
The prime divisors of 34 are 2 and 17.
Video solution of Divisors of 34:
Sum, Product & Number of Divisors of 34
The prime factorization of 34 is given below.
34 = 21 ×171
(i) By the number of divisors formula, we have that the number of divisors of 34 is
=(1+1)(1+1)=2×2=4.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 34 is
$=\dfrac{2^2-1}{2-1} \times \dfrac{17^2-1}{17-1}$
$=\dfrac{4-1}{1} \times \dfrac{289-1}{16}$
$=3 \times 18=54$
(iii) By the product of divisors formula, we have that the product of the divisors of 34 is
=34(Number of divisors of 34)/2
=344/2
=342
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