Perform precise arithmetic operations and analyze integer properties.
Addition (A + B)
Subtraction (A – B)
Multiplication (A × B)
Division (A ÷ B)
Remainder / Modulo (A % B)
Exponentiation (A^B)
Operation Result:
Parity:
Sign:
Primality:
Factors:
Understanding Integers: A Comprehensive Guide
In mathematics, integers are a foundational set of numbers consisting of zero, positive natural numbers, and their additive inverses (negative numbers). Unlike fractions or decimals, integers represent "whole" quantities that do not have a fractional component.
Basic Rules of Integer Arithmetic
When working with integers, particularly negative values, specific rules govern how signs interact during calculation.
Operation
Sign Combination
Resulting Sign
Multiplication
Positive × Positive
Positive (+)
Multiplication
Positive × Negative
Negative (-)
Multiplication
Negative × Negative
Positive (+)
Division
Negative ÷ Positive
Negative (-)
Properties of Integers
Closure Property: The sum, difference, or product of any two integers is always an integer.
Parity: An integer is either "Even" (divisible by 2) or "Odd" (not divisible by 2).
Primality: A positive integer greater than 1 is "Prime" if its only divisors are 1 and itself.
How to Use This Integer Calculator
This tool is designed to provide more than just basic arithmetic. Here is how to interpret the results:
First and Second Integer: Enter any whole numbers (positive or negative).
Operation: Choose between standard addition, subtraction, multiplication, division, the modulo (remainder), or powers.
Analysis: The calculator will automatically determine if the result is even or odd, its primality, and list its factors (for positive results).
Example Calculation
If you input A = 12 and B = 3 with the Division operation:
Result: 4
Parity: Even
Factors: 1, 2, 4
Sign: Positive
Common Questions about Integers
Is zero an integer? Yes, zero is an integer. It is neither positive nor negative and is classified as an even number.
What is the difference between an integer and a whole number? While integers include negative numbers (…, -2, -1, 0, 1, 2, …), whole numbers typically refer only to non-negative integers (0, 1, 2, …).
function calculateIntegers() {
var val1 = document.getElementById("int1").value;
var val2 = document.getElementById("int2").value;
var op = document.getElementById("operation").value;
var resBox = document.getElementById("result-box");
if (val1 === "" || val2 === "") {
alert("Please enter both integers.");
return;
}
var a = parseInt(val1);
var b = parseInt(val2);
var result;
// Perform Operation
switch (op) {
case "add":
result = a + b;
break;
case "subtract":
result = a – b;
break;
case "multiply":
result = a * b;
break;
case "divide":
if (b === 0) {
alert("Error: Division by zero is undefined.");
return;
}
result = Math.floor(a / b);
break;
case "modulo":
if (b === 0) {
alert("Error: Modulo by zero is undefined.");
return;
}
result = a % b;
break;
case "power":
result = Math.pow(a, b);
break;
default:
result = 0;
}
// Display basic result
document.getElementById("res-val").innerText = result;
// Parity
document.getElementById("res-parity").innerText = (result % 2 === 0) ? "Even" : "Odd";
// Sign
if (result > 0) {
document.getElementById("res-sign").innerText = "Positive (+)";
} else if (result 0 && result < 100000) {
document.getElementById("factor-section").style.display = "block";
document.getElementById("res-factors").innerText = getFactors(result).join(", ");
} else if (result <= 0) {
document.getElementById("factor-section").style.display = "none";
} else {
document.getElementById("res-factors").innerText = "Result too large to factorize quickly.";
}
resBox.style.display = "block";
}
function isPrime(n) {
if (n <= 1) return "Not Prime";
if (n <= 3) return "Prime";
if (n % 2 === 0 || n % 3 === 0) return "Not Prime";
for (var i = 5; i * i <= n; i = i + 6) {
if (n % i === 0 || n % (i + 2) === 0) return "Not Prime";
}
return "Prime";
}
function getFactors(n) {
var factors = [];
for (var i = 1; i <= Math.sqrt(n); i++) {
if (n % i === 0) {
factors.push(i);
if (i !== n / i) {
factors.push(n / i);
}
}
}
factors.sort(function(x, y) { return x – y; });
return factors;
}