Divisors and Factors Calculator

Understanding Divisors and Factors

What are Divisors and Factors?

Divisors, also known as factors, are numbers that divide evenly into another number without leaving a remainder. For example, the divisors of 12 are 1, 2, 3, 4, 6, and 12.

Mathematical Definition

Mathematically, we say that \(d\) is a divisor of \(n\) if there exists an integer \(k\) such that:

\[n = d \times k\]

Alternatively, we can express this using modular arithmetic:

\[n \equiv 0 \pmod{d}\]

Finding Divisors

To find all divisors of a number \(n\):

1. Check all numbers from 1 to \(\sqrt{n}\).
2. If \(i\) divides \(n\) evenly, both \(i\) and \(n/i\) are divisors.
3. Include 1 and \(n\) itself as divisors.

Example with Visual Representation

Let's find the divisors of 24:

1. Check numbers up to \(\sqrt{24} \approx 4.9\)
2. Divisors found: 1, 2, 3, 4, 6, 8, 12, 24

This diagram visually represents the divisors of 24, showing that it has 8 divisors and is not a prime number.