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 $\dfrac{35}{n}$ 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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