Prime Factorization Calculator

Factor an integer and derive divisor-count, divisor-sum, Euler totient, and divisor list.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

This calculator factors a positive integer into prime powers and then derives the standard arithmetic functions that come directly from that factorization. It is useful when you want more than just the factor list and need divisor counts, divisor sums, or Euler's totient as well.

It combines Integer to estimate Prime Factorization, Number of Divisors, Sum of Divisors.

Formula & Method

Core equations: If n=\prod p_i^{a_i} then d(n)=\prod(a_i+1),\quad \sigma(n)=\prod\frac{p_i^{a_i+1}-1}{p_i-1},\quad \varphi(n)=n\prod\left(1-\frac{1}{p_i}\right).

Notation used in the formulas: R = Prime Factorization; x_{1} = Integer.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when analyzing divisibility, simplifying ratio and modular problems, or preparing inputs for Euler totient, CRT, and divisor-function style arguments.

Inputs Used

Integer: Used directly in the calculation.

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