Prime Factorization Calculator
Prime Factorization is evaluated from Positive Integer. The calculation reports Prime Factorization, Prime or Composite? and Number of Divisors.
Results
About the Prime Factorization Calculator
The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.
Formula basis:
0 = _n = Math.trunc(Math.abs(parseFloat(number))); _factors = []; _temp = _n; for (var _p = 2; _p * _p <= _temp; _p++) { while (_temp% _p === 0) { _factors.push(_p); _temp = _temp / _p; } } if (_temp > 1) _factors.push(_temp); _map = {}; for (var _i = 0; _i < _factors.length; _i++) { var _f = _factors[_i]; _map[_f] = (_map[_f] || 0) + 1; } _div_count = 1; _sum_div = 1; var _keys = Object.keys(_map); for (var _k = 0; _k < _keys.length; _k++) { var _kk = parseInt(_keys[_k]); var _e = _map[_keys[_k]]; _div_count = _div_count * (_e + 1); var _seg = 0; for (var _j = 0; _j <= _e; _j++) _seg += Math.pow(_kk, _j); _sum_div = _sum_div * _seg; } _fact_str = _keys.map(function(k){ return _map[k] > 1 ? k + '^' + _map[k]: k; }).join(' x '); _is_prime = (_factors.length === 1 && _factors[0] === _n)
Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.
Formula & How It Works
The calculation applies the following relations exactly as recorded in the metadata:
0 = _n = Math.trunc(Math.abs(parseFloat(number))); _factors = []; _temp = _n; for (var _p = 2; _p * _p <= _temp; _p++) { while (_temp% _p === 0) { _factors.push(_p); _temp = _temp / _p; } } if (_temp > 1) _factors.push(_temp); _map = {}; for (var _i = 0; _i < _factors.length; _i++) { var _f = _factors[_i]; _map[_f] = (_map[_f] || 0) + 1; } _div_count = 1; _sum_div = 1; var _keys = Object.keys(_map); for (var _k = 0; _k < _keys.length; _k++) { var _kk = parseInt(_keys[_k]); var _e = _map[_keys[_k]]; _div_count = _div_count * (_e + 1); var _seg = 0; for (var _j = 0; _j <= _e; _j++) _seg += Math.pow(_kk, _j); _sum_div = _sum_div * _seg; } _fact_str = _keys.map(function(k){ return _map[k] > 1 ? k + '^' + _map[k]: k; }).join(' x '); _is_prime = (_factors.length === 1 && _factors[0] === _n)
Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.
Worked Examples
Example 1: Highly Composite Number — 360
Inputs
With Positive Integer = 360 as the stated inputs, the result is Prime or Composite? = false, Number of Divisors = 1 and Sum of All Divisors = 1. Each value corresponds to the declared output fields.
Example 2: Large Prime — 9973
Inputs
With Positive Integer = 9,973 as the stated inputs, the result is Prime or Composite? = false, Number of Divisors = 1 and Sum of All Divisors = 1. Each value corresponds to the declared output fields.
Example 3: Perfect Number Check — 28
Inputs
With Positive Integer = 28 as the stated inputs, the result is Prime or Composite? = false, Number of Divisors = 1 and Sum of All Divisors = 1. Each value corresponds to the declared output fields.
Example 4: Power of 2 — Binary
Inputs
With Positive Integer = 1,024 as the stated inputs, the result is Prime or Composite? = false, Number of Divisors = 1 and Sum of All Divisors = 1. Each value corresponds to the declared output fields.
Common Use Cases
- Find all prime factors of a number
- Check if a number is prime
- Calculate number of divisors
- Find GCD/LCM via prime factorization