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.
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.