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.
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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