1. What is a Divisor?

A divisor of an integer is a number that divides it exactly without leaving a remainder. The number 1 is a special divisor because it divides every integer exactly.

2. How the Calculator Works

The calculator checks all numbers that divide your input exactly:

Where:

• \( n \) — Your input number
• \( d \) — Potential divisor
• \( \mod \) — Modulo operation (remainder after division)

3. Mathematical Explanation

Key Properties:

• Every integer is divisible by 1 and itself
• Prime numbers have exactly two divisors: 1 and themselves
• Composite numbers have more than two divisors
• Zero has infinite divisors (all non-zero integers)

4. Using the Calculator

Instructions: Enter any integer (positive or negative) to find all its divisors. The calculator will always show that 1 is a divisor, plus any other divisors if they exist.

5. Frequently Asked Questions (FAQ)

Q1: Why is 1 a divisor of all numbers?
A: By definition, any number divided by 1 equals itself with no remainder.

Q2: What's special about prime numbers?
A: Primes have exactly two distinct divisors: 1 and themselves.

Q3: How does zero work with divisors?
A: Zero is divisible by all non-zero integers, but division by zero is undefined.

Q4: What about negative numbers?
A: Divisors can be positive or negative, but we typically list only the positive ones.

Q5: What's the largest number of divisors possible?
A: Highly composite numbers like 12, 24, or 120 have more divisors than any smaller number.