The divisors of 75 are those numbers that completely divide 75 with the remainder zero. In this section, we will discuss about divisors of 75.
Table of Contents
Highlights of Divisors of 75
- Divisors of 75: 1, 3, 5, 15, 25 and 75
- Negative divisors of 75: –1, -3, -5, -15, -25 and -75
- Prime divisors of 75: 3 and 5
- Number of divisors of 75: 6
- Sum of divisors of 75: 124
- Product of divisors of 75: 753
What are Divisors of 75
A number n is a divisor of 75 if $\dfrac{75}{n}$ is an integer. Note that if 75/n=m is an integer, then both m and n will be the divisors of 75.
To find the divisors of 75, we need to find the numbers n such that 75/n becomes an integer. We have:
| 75/1=75 | 1, 75 are divisors of 75. |
| 75/3=25 | 3, 25 are divisors of 75 |
| 75/5=15 | 5, 15 are divisors of 75 |
No numbers other than 1, 3, 5, 15, 25, and 75. can divide 75. So we conclude that
|
The divisors of 75 are: 1, 3, 5, 15, 25 and 75 |
Thus, the total number of divisors of 75 is six.
Also Read:
Divisors of 60: The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Divisors of 64: The divisors of 60 are 1, 2, 4, 8, 16, 32, 64.
Divisors of 72: The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Divisors of 100: The divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Negative Divisors of 75
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 75 are 1, 3, 5, 15, 25, and 75, we can say that:
The negative divisors of 75 are -1, -3, -5, -15, -25, and -75.
Prime Divisors of 75
The divisors of 75 are 1, 3, 5, 15, 25, and 75. Among these numbers, only 3 and 5 are prime numbers. So we obtain that:
The prime divisors of 75 are 3 and 5.
Video Solution of Divisors of 75:
Sum, Product & Number of Divisors of 75
The prime factorization of 75 is given below.
75 = 31 × 52
(i) By the number of divisors formula, we have that the number of divisors of 75 is
=(1+1)(2+1)=2×3=6.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 75 is
$=\dfrac{3^2-1}{3-1} \times \dfrac{5^3-1}{5-1}$
$=\dfrac{9-1}{2} \times \dfrac{125-1}{4}$
$=4 \times 31=124$
(iii) By the product of divisors formula, we have that the product of the divisors of 75 is
=75(Number of divisors of 75)/2
=756/2
=753
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FAQs on Divisors of 75
Answer: The divisors of 75 are 1, 3, 5, 15, 25, and 75.
Answer: The sum of the divisors of 75 is (32-1)/(3-1) × (53-1)/(5-1) = 4×31 = 124.
