Sum of Divisors
The sum of divisors of a positive integer n is denoted by σ(n), where σ is the Euler’s Totient Function. σ(n) is calculated by using the following formula:
σ(n) = 1 + n + ∑d|n, d≠1, d≠n d
Where d is the divisor of n.
Let’s understand this by taking examples.
Example 1: For n = 6, find the sum of divisors.
Solution:
Divisors of 6 are: 1, 2, 3, 6
σ(n) = 1 + 2 + 3 + 6 = 12
Example 2: Find σ(15).
Solution:
Divisors of 15 are: 1, 2, 4, 8, 16
σ(n) = 1 + 2 + 4 + 8 + 16 = 31
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Divisors in Maths
Divisor is the number from which we divide the dividend to determine the quotient and remainder. In arithmetic, division is one of the four fundamental operations; other operations are addition, subtraction, and multiplication.
Divisors in Number Theory are integers that divides another integer without leaving the remainder is also called a divisor.
In this article, we will discuss both definitions of a divisor, including the general, and the definition in number theory. We will also explore various properties and examples related to divisors and discuss concepts such as prime divisors, the number of divisors, the sum of divisors, and the difference between a divisor and a factor.
Table of Content
- What are Divisors?
- Properties of Divisors
- Divisors and Dividends
- Divisor in Number Theory
- Examples of Divisors
- What are Prime Divisors?
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