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.
Table of Contents
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 $\dfrac{35}{n}$ 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.
Video solution of Divisors of 35:
Sum, Product & Number of Divisors of 35
The prime factorization of 35 is given below.
35 = 51 ×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
$=\dfrac{5^2-1}{5-1} \times \dfrac{7^2-1}{7-1}$
$=\dfrac{25-1}{4} \times \dfrac{49-1}{6}$
$=6 \times 8=48$
(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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