A number N is an Armstrong Number or narcissistic number if it is equal to the sum of its own digits raised to the power of the number of digits.

"); $('#result1').append("For Example - 153 = 1^3 + 5^3 + 3^3"); } function isPrime(num) { var n, i, flag = true; n = parseInt(num); for(i = 2; i <= n - 1; i++) { if (n % i === 0) { flag = false; break; } } if(flag) { $("#result2").append("" + num + " is Prime Number

"); } else { $("#result2").append("" + num + " is not Prime Number

"); } $('#result2').append("

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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A natural number greater than 1 that is not prime is called a composite number.

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For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 6 is composite because it is the product of two numbers (2 × 3) that are both smaller than 6.

"); $("#result2").append("Prime factors of " + num + " is

"); findPrimeFactors (num); $("#result2").append("

"); $("#result2").append("Distinct Prime factors of " + num + " is

"); distinct_prime_factors(num); } function findPrimeFactors (num) { var primeFactors = []; while (num % 2 === 0) { primeFactors.push(2); num = num / 2; } var sqrtNum = Math.sqrt(num); for (var i = 3; i <= sqrtNum; i++) { while (num % i === 0) { primeFactors.push(i); num = num / i; } } if (num > 2) { primeFactors.push(num); } for(var j = 0; j < primeFactors.length; j++) { $("#result2").append(primeFactors[j]); if(j != (primeFactors.length - 1)) { $("#result2").append(", "); } } } function distinct_prime_factors(num) { function is_prime(num) { for (let i = 2; i <= Math.sqrt(num); i++) { if (num % i === 0) return false; } return true; } const result = []; for (let i = 2; i <= num; i++) { while (is_prime(i) && num % i === 0) { if (!result.includes(i)) result.push(i); num /= i; } } for(var j = 0; j < result.length; j++) { $("#result2").append(result[j]); if(j != (result.length - 1)) { $("#result2").append(", "); } } } function factorial(num) { if(num > 100) { $("#result3").append("" + num + " is too large for Factorial.

"); return; } $("#result3").append(" Factorial of " + num + " is = " + fact(num) + "

"); $("#result3").append("

In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n:

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"); $('#result3').append("

For example,

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"); } function fact(n) { if (n === 0) { return 1; } else { return n * fact( n - 1 ); } } function fabonacciSeries(num) { var i; var fib = []; // Initialize array! fib[0] = 0; fib[1] = 1; if(num.toString().length > 2) { $("#result4").append("" + num + " is too large for Fibonacci.

"); return; } $("#result4").append("First " + num + "th Fibonacci Series.

"); $("#result4").append(fib[0] + ", " + fib[1] + ", "); for (i = 2; i < num; i++) { // Next fibonacci number = previous + one before previous // Translated to JavaScript: fib[i] = fib[i - 2] + fib[i - 1]; $("#result4").append(fib[i]); if(i != (num - 1)) { $("#result4").append(", "); } } $("#result4").append("

"); $("#result4").append("

Fibonacci Series is a series of numbers where the first two Fibonacci numbers are 0 and 1, and each subsequent number is the sum of the previous two. Its recurrence relation is given by Fn = Fn-1 + Fn-2.

"); } function palindrome(num) { var rem, temp, final = 0; temp = num; while(num > 0) { rem = num % 10; num = parseInt(num / 10); final = final * 10 + rem; } if(final == temp) { $("#result5").append(" Number " + temp + " is Palindrome

"); } else { $("#result5").append(" Number " + temp + " is not palindrome

"); } $("#result5").append('

A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward or forward. The word “palindrome” was first coined by the English playwright Ben Jonson in the 17th century, from the Greek roots palin (“again”) and dromos (“way, direction”).

'); } function happy(number) { var m, digit; while(number != 1 && number != 4) { m = 0 ; while (number > 0) { digit = number % 10 ; m += digit * digit ; number = (number - digit) / 10 ; } number = m; } return number; } function happyNumbers(num) { var cnt = num; var number = 1; if(num.toString().length > 3) { return; } $("#result6").append("First " + num + " happy numbers.

"); while(cnt-- > 0) { while(!(happy(number) == 1)) number++; $("#result6").append(number + ", ") ; number++; } $("#result6").append("

"); } function isHappyNumber(num) { if(num.toString().length > 4) { $("#result6").append("" + num + " is too large for Happy Numbers.

"); return; } var result = happy(num); //Happy number always ends with 1 if(result == 1) $("#result6").append(num + " is a happy number"); //Unhappy number ends in a cycle of repeating numbers which contains 4 else if(result == 4) $("#result6").append(num + " is not a happy number"); $("#result6").append("

"); $("#result6").append('

A happy number is defined by the following process:

Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers.

'); } function gapFulNumber(num) { if(num.toString().length > 3) { return; } var f = num.toString().charAt(0); var l = num.toString().charAt(2); var s = Number(f + l); if(num % s == 0) { $("#result7").append(num + " is GapFul Number."); } else { $("#result7").append(num + " is not GapFul Number."); } $("#result7").append("

"); $("#result7").append('

Numbers (positive integers expressed in base ten) that are (evenly) divisible by the number formed by the first and last digit are known as gapful numbers.

'); } function check(e) { if(e.keyCode == 8) { for(var i = 1; i <= 6; i++) { $("#result" + i).empty(); } $(".armstr").delay(500).fadeOut(); $(".isPrime").delay(1000).fadeOut(); $(".factorial").delay(1500).fadeOut(); $(".fabonacciSeries").delay(2000).fadeOut(); $(".palindrome").delay(2500).fadeOut(); $(".happyNumbers").delay(3000).fadeOut(); $(".gapFulNumbers").delay(3500).fadeOut(); } }

Number Problems