Divisors of 35

A number is said to be a divisor of 35 if that number completely divides 35 with the remainder zero. In this section, we will discuss about divisors of 35.

Highlights of Divisors of 35

  • Divisors of 35: 1, 5, 7 and 35
  • Negative divisors of 35: -1, -5, -7 and -35
  • Prime divisors of 35: 5 and 7
  • Number of divisors of 35: 4
  • Sum of divisors of 35: 48
  • Product of divisors of 35: 352

What are Divisors of 35

A number n is a divisor of 35 if $\frac{35}{n}$ is an integer. Note that if 35/n=m is an integer, then both m and n will be the divisors of 35.

To find the divisors of 35, we need to find the numbers n such that 35/n becomes an integer. We have:

35/1=35 1, 35 are divisors of 35.
35/5=7 5, 7 are divisors of 35

No numbers other than 1, 5, 7 and 35 can divide 35. So we conclude that

The divisors of 35 are:

1, 5, 7 and 35.

Thus, the total number of divisors of 35 is four.

 

Negative Divisors of 35

We know that if m is a divisor of a number, then -m is also a divisor of that number.

As the divisors of 35 are 1, 5, 7, and 35, we can say that:

The negative divisors of 35 are -1, -5, -7, and –35.

 

Prime Divisors of 35

The divisors of 35 are 1, 5, 7, and 35. Among these numbers, only 5 and 7 are prime numbers. So we obtain that:

The prime divisors of 35 are 5 and 7.

 

Key Things

The prime factorization of 35 is given below.

35 = 5×71

(i) By the number of divisors formula, we have that the number of divisors of 35 is

=(1+1)(1+1)=2×2=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 35 is

$=\frac{5^2-1}{5-1} \times \frac{7^2-1}{7-1}$

$=\frac{25-1}{4} \times \frac{49-1}{6}$

$=6 \times 8=48$

(iii) By the product of divisors formula, we have that the product of the divisors of 35 is

=35(Number of divisors of 35)/2

=354/2

=352

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