The divisors of 25 are 1, 5, and 25. The divisors of 25 are those numbers that completely divide 25 with the remainder zero. Here we will discuss divisors of 25.
Table of Contents
Highlights of Divisors of 25
- Divisors of 25: 1, 5 and 25
- Negative divisors of 25: -1, -5 and -25
- Prime divisors of 25: 5
- Number of divisors of 25: 3
- Sum of divisors of 25: 31
- Product of divisors of 25: 253/2 =125.
| How to find divisors of 25? To find the divisors of 25, we need to find the number n such that 25/n = an integer. As 25/4 is not an integer, 4 is not a divisor of 25. On the other hand, 5 is a divisor of 25 as 25/5=5 is an integer. |
What are the Divisors of 25
Using the rule Dividend ÷ Divisor = Quotient, let us find the list of divisors of 25. Note that we have:
| 25/1=25 | 1, 25 are divisors of 25. |
| 25/5=5 | 5 is a divisor of 25 |
No numbers other than 1, 5, and 25 can divide 25. So the divisors of 25 are 1, 5, and 25. Hence the total number of divisors of 25 is three.
Properties of Divisors of 25
- Negative Divisors: We know that if m is a divisor of a number, then -m is also a divisor of that number. As the divisors of 25 are 1, 5, and 25, so the negative divisors of 25 are -1, -5, and –25.
- Prime Divisors: Among the divisors of 25, only 5 is a prime number. So we conclude that 5 is the only prime divisor of 25.
Video solution of Divisors of 25:
Sum, Product & Number of Divisors of 25
The prime factorization of 25 is given below.
25 = 52
(i) By the number of divisors formula, we have that the number of divisors of 25 is
=(2+1)=3.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 25 is
$=\dfrac{5^3-1}{5-1}$
$=\dfrac{125-1}{4}$
$=31$
(iii) By the product of divisors formula, we have that the product of the divisors of 25 is
=25(Number of divisors of 25)/2
=253/2
=125
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