# 10 Examples of Divisors in Mathematics

In **mathematics**, **divisors** are numbers that evenly divide another number without leaving a remainder. They play a important role in number theory, factorization, and many areas of mathematics.

In this article, we will explore ten examples of divisors in mathematics, highlighting their significance and applications.

**Examples of Divisors **

These are ten examples of divisors.

**1: Understanding Divisors**

Divisors, also known as factors, are numbers that divide another number without leaving a remainder.

For example, the divisors of 12 are 1, 2, 3, 4, 6, and 12.

**2: Positive Divisors**

Positive divisors are divisors that are greater than 0.

For example, the positive divisors of 18 are 1, 2, 3, 6, 9, and 18.

**3: Negative Divisors**

Negative divisors are divisors that are less than 0. Negative divisors are less commonly used but are still valid.

For example, the negative divisors of -12 are -1, -2, -3, -4, -6, and -12.

**4: Prime Numbers**

Prime numbers have only two positive divisors, 1 and themselves.

Examples include 2, 3, 5, and 7.

**5: Perfect Numbers**

Perfect numbers are numbers that are equal to the sum of their positive divisors (excluding themselves). The smallest perfect number is 6 (divisors: 1, 2, 3).

**6: Amicable Numbers**

Amicable numbers are pairs of numbers in which each number is equal to the sum of the positive divisors of the other.

An example is the pair (220, 284).

**7: Divisor Functions**

Mathematicians use divisor functions like the sum of divisors (sigma function) and the number of divisors function to analyze divisors’ properties.

**8: Divisors in Factorization**

Divisors are crucial in factorization, where numbers are expressed as products of their prime divisors.

For example, the prime factorization of 36 is 2^2 * 3^2.

**9: Divisors in Geometry**

In geometry, divisors play a role in defining geometric shapes.

For example, a rectangle with dimensions 6 units by 4 units has divisors of its area: 1, 2, 3, 4, 6, 8, 12, and 24.

**10: Real-World Applications of Divisors**

Divisors are used in various real-world applications, such as calculating the number of ways to distribute objects or finding common denominators in fractions.

Understanding divisors is essential in number theory, factorization, and solving mathematical problems.

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