Divisors of 34

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 $\frac{34}{n}$ 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.

 

Key Things

The prime factorization of 34 is given below.

34 = 2×171

(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

$=\frac{2^2-1}{2-1} \times \frac{17^2-1}{17-1}$

$=\frac{4-1}{1} \times \frac{289-1}{16}$

$=3 \times 18=54$

(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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