Number Theory

Prime factorisation

Primes, divisor count and sum, φ\varphi, μ\mu, and every divisor in pairs.

For checking your work after you’ve tried it yourself.

Step 1:
Type a number

Any whole number from 1 to 101810^{18}.

Step 2:
Press Factorise

Or press Enter.

Step 3:
Read and check

Compare with your working, then open Do it by hand.
What it does.
Every whole number bigger than 1 can be written as primes multiplied together in exactly one way. This tool finds that way, then uses it for four facts: how many divisors there are (τ\tau), what they add up to (σ\sigma), how many numbers up to it share no factor with it (φ\varphi), and the Möbius value (μ\mu). It also lists every divisor next to its partner.
When it helps.
Checking a factorisation or a divisor count you worked out yourself.
What it won’t do.
It checks numbers; it doesn't solve problems. It stops above 101810^{18}, and for very large numbers the by-hand card says honestly when paper wouldn't manage.
Example.
360=23×32×5360 = 2^3 \times 3^2 \times 5, so it has (3+1)(2+1)(1+1)=24(3+1)(2+1)(1+1) = 24 divisors.

Spaces and commas are ignored.

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